# Sequences and Series

## by The Ohio State University

This course material is only available in the iTunes U app on iPhone or iPad.

#### Course Description

Sequences and Series will challenge us to think very carefully about "infinity." What does it mean to add up an unending list of numbers? How can an infinite task result in a finite answer? These questions lead us to some very deep concepts, but also to some powerful computational tools which are used not only in math but in many quantitative disciplines.

This course is a first and friendly introduction to sequences, infinite series, convergence tests, and Taylor series. It is suitable for someone who has seen just a bit of calculus before.

Name | Description | Time | Price | ||
---|---|---|---|---|---|

1 | CAPTIONED: Why is monotonicity important for the AST? - Week 4 - Lecture 8 | -- | 5:44 | Free | View in iTunes |

2 | CAPTIONED: Why is the radius of convergence of 1/(1+x²) so small? - Week 6 - Lecture 6 | -- | 9:52 | Free | View in iTunes |

3 | CAPTIONED: Why is absolute convergence an important concept? - Week 4 - Lecture 3 | -- | 3:37 | Free | View in iTunes |

4 | CAPTIONED: Why is this all so vague… or coarse? - Week 4 - Lecture 13 | -- | 6:06 | Free | View in iTunes |

5 | CAPTIONED: Why might I believe that ∑ (xⁿ)/(n!) is eˣ? - Week 5 - Lecture 10 | -- | 4:14 | Free | View in iTunes |

6 | CAPTIONED: Why is e irrational? - Week 4 - Lecture 10 | -- | 8:41 | Free | View in iTunes |

7 | CAPTIONED: Why are alternating series important? - Week 4 - Lecture 9 | -- | 6:09 | Free | View in iTunes |

8 | CAPTIONED: Why do absolutely convergent series just plain converge? - Week 4 - Lecture 2 | -- | 5:21 | Free | View in iTunes |

9 | CAPTIONED: Why have we been assuming the terms are positive? - Week 4 - Lecture 1 | -- | 3:36 | Free | View in iTunes |

10 | CAPTIONED: Why don't I love the root test? - Week 3 - Lecture 6 | -- | 3:41 | Free | View in iTunes |

11 | CAPTIONED: Why does ∑ n/(n+1) diverge? - Week 2 - Lecture 6 | -- | 10:15 | Free | View in iTunes |

12 | CAPTIONED: Why does a power series converge absolutely? - Week 5 - Lecture 2 | -- | 4:53 | Free | View in iTunes |

13 | CAPTIONED: What is the value of ∑ rᵏ? - Week 2 - Lecture 3 | -- | 9:31 | Free | View in iTunes |

14 | CAPTIONED: What is the alternating series test? - Week 4 - Lecture 6 | -- | 11:04 | Free | View in iTunes |

15 | CAPTIONED: Why does ∑ (1/2)ᵏ = 2? - Week 2 - Lecture 2 | -- | 5:20 | Free | View in iTunes |

16 | CAPTIONED: Why can people get away with writing ∑ₙ aₙ? - Week 4 - Lecture 12 | -- | 4:31 | Free | View in iTunes |

17 | CAPTIONED: When is a sequence bounded? - Week 1 - Lecture 12 | -- | 8:28 | Free | View in iTunes |

18 | CAPTIONED: When do two series share the same fate? - Week 4 - Lecture 11 | -- | 5:53 | Free | View in iTunes |

19 | CAPTIONED: When is a sequence increasing? - Week 1 - Lecture 13 | -- | 4:48 | Free | View in iTunes |

20 | CAPTIONED: What is Week 4 all about? - Week 4 Introduction | -- | 1:15 | Free | View in iTunes |

21 | CAPTIONED: What will happen in Week 3? - Week 3 Introduction | -- | 1:22 | Free | View in iTunes |

22 | CAPTIONED: What is the Taylor series of f around zero? - Week 6 - Lecture 2 | -- | 10:12 | Free | View in iTunes |

23 | CAPTIONED: What is the value of ∑ rᵏ for k = m to infinity? - Week 2 - Lecture 4 | -- | 7:05 | Free | View in iTunes |

24 | CAPTIONED: What is this last week about? - Week 6 Introduction | -- | 2:11 | Free | View in iTunes |

25 | CAPTIONED: What is the Taylor series of f centered around a? - Week 6 - Lecture 3 | -- | 4:39 | Free | View in iTunes |

26 | CAPTIONED: What is the Taylor series for sin x around zero? - Week 6 - Lecture 4 | -- | 4:36 | Free | View in iTunes |

27 | CAPTIONED: What is a formula for the Fibonacci numbers? - Week 5 - Lecture 13 | -- | 12:12 | Free | View in iTunes |

28 | CAPTIONED: What is the limit of a sequence? - Week 1 - Lecture 7 | -- | 4:43 | Free | View in iTunes |

29 | CAPTIONED: What is Taylor's theorem? - Week 6 - Lecture 5 | -- | 11:42 | Free | View in iTunes |

30 | CAPTIONED: What is the Monotone Convergence Theorem? - Week 1 - Lecture 14 | -- | 1:47 | Free | View in iTunes |

31 | CAPTIONED: What is the comparison test? - Week 2 - Lecture 9 | -- | 8:26 | Free | View in iTunes |

32 | CAPTIONED: What is ∑ 1/((k+1) k)? - Week 2 - Lecture 5 | -- | 10:11 | Free | View in iTunes |

33 | CAPTIONED: What is better than a linear approximation? - Week 6 - Lecture 1 | -- | 14:12 | Free | View in iTunes |

34 | CAPTIONED: What is an alternating series? - Week 4 - Lecture 5 | -- | 4:10 | Free | View in iTunes |

35 | CAPTIONED: What is conditional convergence? - Week 4 - Lecture 4 | -- | 2:51 | Free | View in iTunes |

36 | CAPTIONED: What is a sequence? - Week 1 - Lecture 1 | -- | 4:06 | Free | View in iTunes |

37 | CAPTIONED: What is an arithmetic progression? - Week 1 - Lecture 5 | -- | 2:18 | Free | View in iTunes |

38 | CAPTIONED: What is a real analytic function? - Week 6 - Lecture 10 | -- | 4:54 | Free | View in iTunes |

39 | CAPTIONED: What if the radius of convergence is zero? - Week 5 - Lecture 6 | -- | 3:26 | Free | View in iTunes |

40 | CAPTIONED: What is a power series centered around a? - Week 5 - Lecture 7 | -- | 4:07 | Free | View in iTunes |

41 | CAPTIONED: What is a geometric progression? - Week 1 - Lecture 6 | -- | 4:26 | Free | View in iTunes |

42 | CAPTIONED: What happens when I rearrange the terms in a series? - Week 4 - Lecture 14 | -- | 7:19 | Free | View in iTunes |

43 | CAPTIONED: In what sense is 9 + 90 + 900 + ... meaningful? - Week 2 - Lecture 13 | -- | 9:41 | Free | View in iTunes |

44 | CAPTIONED: What does ∑ aₖ = L mean? - Week 2 - Lecture 1 | -- | 3:54 | Free | View in iTunes |

45 | CAPTIONED: What if the radius of convergence is infinity? - Week 5 - Lecture 5 | -- | 4:03 | Free | View in iTunes |

46 | CAPTIONED: Is there a sequence that includes every real number? - Week 1 - Lecture 17 | -- | 5:20 | Free | View in iTunes |

47 | CAPTIONED: What happens if I transform 1/(1-x)? - Week 5 - Lecture 12 | -- | 6:59 | Free | View in iTunes |

48 | CAPTIONED: What happens in Week 2? - Week 2 Introduction | -- | 1:20 | Free | View in iTunes |

49 | CAPTIONED: What happens if I multiply two power series? - Week 5 - Lecture 11 | -- | 9:28 | Free | View in iTunes |

50 | CAPTIONED: How far out can you build a one-sided bridge? - Week 3 - Lecture 11 | -- | 10:44 | Free | View in iTunes |

51 | CAPTIONED: What does the ratio test say? - Week 3 - Lecture 2 | -- | 7:52 | Free | View in iTunes |

52 | CAPTIONED: In what sense does ∑ 9 × 10⁽⁻ⁿ⁾ equal one? - Week 2 - Lecture 12 | -- | 5:06 | Free | View in iTunes |

53 | CAPTIONED: What are power series? - Week 5 Introduction | -- | 3:04 | Free | View in iTunes |

54 | CAPTIONED: Visually, what is the limit of a sequence? - Week 1 - Lecture 8 | -- | 1:43 | Free | View in iTunes |

55 | CAPTIONED: Is it easy to find the limit of a sequence? - Week 1 - Lecture 9 | -- | 8:03 | Free | View in iTunes |

56 | CAPTIONED: Is there a sequence that includes every integer? - Week 1 - Lecture 16 | -- | 4:46 | Free | View in iTunes |

57 | CAPTIONED: How else can I show ∑ 1/n diverges? - Week 3 - Lecture 8 | -- | 5:05 | Free | View in iTunes |

58 | CAPTIONED: Does ∑ n⁵/4ⁿ converge? - Week 3 - Lecture 1 | -- | 13:39 | Free | View in iTunes |

59 | CAPTIONED: How is Taylor's theorem like the mean value theorem? - Week 6 - Lecture 7 | -- | 8:04 | Free | View in iTunes |

60 | CAPTIONED: How should I go about checking convergence? - Week 4 - Lecture 7 | -- | 1:42 | Free | View in iTunes |

61 | CAPTIONED: How is a sequence presented? - Week 1 - Lecture 2 | -- | 5:46 | Free | View in iTunes |

62 | CAPTIONED: How does n! compare to nⁿ? - Week 3 - Lecture 5 | -- | 6:12 | Free | View in iTunes |

63 | CAPTIONED: How do Taylor series provide intuition for limits? - Week 6 - Lecture 9 | -- | 11:04 | Free | View in iTunes |

64 | CAPTIONED: How do sequences help with the square root of two? - Week 1 - Lecture 11 | -- | 3:02 | Free | View in iTunes |

65 | CAPTIONED: How do I find the radius of convergence? - Week 5 - Lecture 4 | -- | 3:26 | Free | View in iTunes |

66 | CAPTIONED: How complicated might the interval of convergence be? - Week 5 - Lecture 3 | -- | 5:15 | Free | View in iTunes |

67 | CAPTIONED: How can the Monotone Convergence Theorem help? - Week 1 - Lecture 15 | -- | 5:45 | Free | View in iTunes |

68 | CAPTIONED: How can integrating help us to address convergence? - Week 3 - Lecture 7 | -- | 12:27 | Free | View in iTunes |

69 | CAPTIONED: How can we build new sequences from old sequences? - Week 1 - Lecture 4 | -- | 3:24 | Free | View in iTunes |

70 | CAPTIONED: For which values does a power series converge? - Week 5 - Lecture 1 | -- | 3:48 | Free | View in iTunes |

71 | CAPTIONED: How can grouping make the comparison test even better? - Week 2 - Lecture 10 | -- | 6:20 | Free | View in iTunes |

72 | CAPTIONED: Does the ratio test always work? - Week 3 - Lecture 3 | -- | 5:35 | Free | View in iTunes |

73 | CAPTIONED: How can I succeed in this course? - Week 1 Introduction | -- | 1:08 | Free | View in iTunes |

74 | CAPTIONED: Does ∑ 1/n converge or diverge? - Week 2 - Lecture 7 | -- | 6:40 | Free | View in iTunes |

75 | CAPTIONED: How are real analytic functions like holograms? - Week 6 - Lecture 11 | -- | 4:24 | Free | View in iTunes |

76 | CAPTIONED: For some epsilon, how large need N be? - Week 1 - Lecture 10 | -- | 4:10 | Free | View in iTunes |

77 | CAPTIONED: Does the series ∑ (sin² k)/(2ᵏ) converge or diverge? - Week 2 - Lecture 8 | -- | 3:52 | Free | View in iTunes |

78 | CAPTIONED: Does ∑ 1/nᵖ converge? - Week 3 - Lecture 9 | -- | 8:07 | Free | View in iTunes |

79 | CAPTIONED: Does ∑ 1/n² converge? - Week 2 - Lecture 11 | -- | 9:00 | Free | View in iTunes |

80 | CAPTIONED: Does ∑ 1/(n log n) converge? - Week 3 - Lecture 10 | -- | 7:39 | Free | View in iTunes |

81 | CAPTIONED: Does ∑ (n!)/(nⁿ) converge? - Week 3 - Lecture 4 | -- | 9:05 | Free | View in iTunes |

82 | CAPTIONED: Approximately, what is cos x when x is near zero? - Week 6 - Lecture 8 | -- | 8:15 | Free | View in iTunes |

83 | CAPTIONED: Can I integrate a power series? - Week 5 - Lecture 9 | -- | 6:18 | Free | View in iTunes |

84 | CAPTIONED: Can I differentiate a power series? - Week 5 - Lecture 8 | -- | 3:31 | Free | View in iTunes |

85 | CAPTIONED: Can the same sequence be presented in different ways? - Week 1 - Lecture 3 | -- | 3:40 | Free | View in iTunes |

86 | Instructor Information | -- | -- | Free | View in iTunes |

87 | Sequences and Series Textbook | -- | -- | Free | View in iTunes |

88 | How can I succeed in this course? - Week 1 Introduction | -- | 1:08 | Free | View in iTunes |

89 | Sequences: What is a sequence? | -- | -- | Free | View in iTunes |

90 | What is a sequence? - Week 1 - Lecture 1 | -- | 4:06 | Free | View in iTunes |

91 | How is a sequence presented? - Week 1 - Lecture 2 | -- | 5:46 | Free | View in iTunes |

92 | Can the same sequence be presented in different ways? - Week 1 - Lecture 3 | -- | 3:40 | Free | View in iTunes |

93 | Sequences: What are some examples of sequences? | -- | -- | Free | View in iTunes |

94 | How can we build new sequences from old sequences? - Week 1 - Lecture 4 | -- | 3:24 | Free | View in iTunes |

95 | What is an arithmetic progression? - Week 1 - Lecture 5 | -- | 2:18 | Free | View in iTunes |

96 | What is a geometric progression? - Week 1 - Lecture 6 | -- | 4:26 | Free | View in iTunes |

97 | Sequences: What is the limit of a sequence? | -- | -- | Free | View in iTunes |

98 | What is the limit of a sequence? - Week 1 - Lecture 7 | -- | 4:43 | Free | View in iTunes |

99 | Visually, what is the limit of a sequence? - Week 1 - Lecture 8 | -- | 1:43 | Free | View in iTunes |

100 | Is it easy to find the limit of a sequence? - Week 1 - Lecture 9 | -- | 8:03 | Free | View in iTunes |

101 | For some epsilon, how large need N be? - Week 1 - Lecture 10 | -- | 4:10 | Free | View in iTunes |

102 | Sequences: Why do we care? | -- | -- | Free | View in iTunes |

103 | How do sequences help with the square root of two? - Week 1 - Lecture 11 | -- | 3:02 | Free | View in iTunes |

104 | Sequences: What other properties might a sequence have? | -- | -- | Free | View in iTunes |

105 | When is a sequence bounded? - Week 1 - Lecture 12 | -- | 8:28 | Free | View in iTunes |

106 | When is a sequence increasing? - Week 1 - Lecture 13 | -- | 4:48 | Free | View in iTunes |

107 | What is the Monotone Convergence Theorem? - Week 1 - Lecture 14 | -- | 1:47 | Free | View in iTunes |

108 | How can the Monotone Convergence Theorem help? - Week 1 - Lecture 15 | -- | 5:45 | Free | View in iTunes |

109 | Sequences: How big can sequences be? | -- | -- | Free | View in iTunes |

110 | Is there a sequence that includes every integer? - Week 1 - Lecture 16 | -- | 4:46 | Free | View in iTunes |

111 | Is there a sequence that includes every real number? - Week 1 - Lecture 17 | -- | 5:20 | Free | View in iTunes |

112 | Sequences: Congratulations! | -- | -- | Free | View in iTunes |

113 | Series: Week 2 - Series | -- | -- | Free | View in iTunes |

114 | What happens in Week 2? - Week 2 Introduction | -- | 1:20 | Free | View in iTunes |

115 | Series: What is a series? | -- | -- | Free | View in iTunes |

116 | What does ∑ aₖ = L mean? - Week 2 - Lecture 1 | -- | 3:54 | Free | View in iTunes |

117 | Why does ∑ (1/2)ᵏ = 2? - Week 2 - Lecture 2 | -- | 5:20 | Free | View in iTunes |

118 | Series: What is a geometric series? | -- | -- | Free | View in iTunes |

119 | What is the value of ∑ rᵏ? - Week 2 - Lecture 3 | -- | 9:31 | Free | View in iTunes |

120 | What is the value of ∑ rᵏ for k = m to infinity? - Week 2 - Lecture 4 | -- | 7:05 | Free | View in iTunes |

121 | Series: What is a telescoping series? | -- | -- | Free | View in iTunes |

122 | What is ∑ 1/((k+1) k)? - Week 2 - Lecture 5 | -- | 10:11 | Free | View in iTunes |

123 | Series: What about more complicated series? | -- | -- | Free | View in iTunes |

124 | Series: How can I prove that some series diverge? | -- | -- | Free | View in iTunes |

125 | Why does ∑ n/(n+1) diverge? - Week 2 - Lecture 6 | -- | 10:15 | Free | View in iTunes |

126 | Series: What is the harmonic series? | -- | -- | Free | View in iTunes |

127 | Does ∑ 1/n converge or diverge? - Week 2 - Lecture 7 | -- | 6:40 | Free | View in iTunes |

128 | Series: What about more complicated series? | -- | -- | Free | View in iTunes |

129 | Does the series ∑ (sin² k)/(2ᵏ) converge or diverge? - Week 2 - Lecture 8 | -- | 3:52 | Free | View in iTunes |

130 | What is the comparison test? - Week 2 - Lecture 9 | -- | 8:26 | Free | View in iTunes |

131 | How can grouping make the comparison test even better? - Week 2 - Lecture 10 | -- | 6:20 | Free | View in iTunes |

132 | Does ∑ 1/n² converge? - Week 2 - Lecture 11 | -- | 9:00 | Free | View in iTunes |

133 | Series: What is point nine repeating? | -- | -- | Free | View in iTunes |

134 | In what sense does ∑ 9 × 10⁽⁻ⁿ⁾ equal one? - Week 2 - Lecture 12 | -- | 5:06 | Free | View in iTunes |

135 | In what sense is 9 + 90 + 900 + ... meaningful? - Week 2 - Lecture 13 | -- | 9:40 | Free | View in iTunes |

136 | Series: By the end of the week... | -- | -- | Free | View in iTunes |

137 | Convergence Tests: Week 3 - Convergence tests | -- | -- | Free | View in iTunes |

138 | What will happen in Week 3? - Week 3 Introduction | -- | 1:22 | Free | View in iTunes |

139 | Convergence Tests: What is the ratio test? | -- | -- | Free | View in iTunes |

140 | Does ∑ n⁵/4ⁿ converge? - Week 3 - Lecture 1 | -- | 13:39 | Free | View in iTunes |

141 | What does the ratio test say? - Week 3 - Lecture 2 | -- | 7:52 | Free | View in iTunes |

142 | Does the ratio test always work? - Week 3 - Lecture 3 | -- | 5:35 | Free | View in iTunes |

143 | Convergence Tests: How do I apply the ratio test? | -- | -- | Free | View in iTunes |

144 | Convergence Tests: What is the ratio test good for? | -- | -- | Free | View in iTunes |

145 | Does ∑ (n!)/(nⁿ) converge? - Week 3 - Lecture 4 | -- | 9:05 | Free | View in iTunes |

146 | How does n! compare to nⁿ? - Week 3 - Lecture 5 | -- | 6:12 | Free | View in iTunes |

147 | Convergence Tests: What is the root test? | -- | -- | Free | View in iTunes |

148 | Why don't I love the root test? - Week 3 - Lecture 6 | -- | 3:41 | Free | View in iTunes |

149 | Convergence Tests: What is the integral test? | -- | -- | Free | View in iTunes |

150 | How can integrating help us to address convergence? - Week 3 - Lecture 7 | -- | 12:27 | Free | View in iTunes |

151 | How else can I show ∑ 1/n diverges? - Week 3 - Lecture 8 | -- | 5:05 | Free | View in iTunes |

152 | Convergence Tests: What are p-series? | -- | -- | Free | View in iTunes |

153 | Does ∑ 1/nᵖ converge? - Week 3 - Lecture 9 | -- | 8:07 | Free | View in iTunes |

154 | Does ∑ 1/(n log n) converge? - Week 3 - Lecture 10 | -- | 7:39 | Free | View in iTunes |

155 | Convergence Tests: How large can the overhang in a stack of blocks be? | -- | -- | Free | View in iTunes |

156 | How far out can you build a one-sided bridge? - Week 3 - Lecture 11 | -- | 10:44 | Free | View in iTunes |

157 | Convergence Tests: By the end of the week.. | -- | -- | Free | View in iTunes |

158 | Alternating Series: Week 4- Alternating Series | -- | -- | Free | View in iTunes |

159 | What is Week 4 all about? - Week 4 Introduction | -- | 1:15 | Free | View in iTunes |

160 | Why have we been assuming the terms are positive? - Week 4 - Lecture 1 | -- | 3:36 | Free | View in iTunes |

161 | Alternating Series: What is absolute convergence? | -- | -- | Free | View in iTunes |

162 | Why do absolutely convergent series just plain converge? - Week 4 - Lecture 2 | -- | 5:21 | Free | View in iTunes |

163 | Why is absolute convergence an important concept? - Week 4 - Lecture 3 | -- | 3:37 | Free | View in iTunes |

164 | What is conditional convergence? - Week 4 - Lecture 4 | -- | 2:51 | Free | View in iTunes |

165 | Alternating Series: What is an alternating series? | -- | -- | Free | View in iTunes |

166 | What is an alternating series? - Week 4 - Lecture 5 | -- | 4:09 | Free | View in iTunes |

167 | What is the alternating series test? - Week 4 - Lecture 6 | -- | 11:03 | Free | View in iTunes |

168 | How should I go about checking convergence? - Week 4 - Lecture 7 | -- | 1:42 | Free | View in iTunes |

169 | Why is monotonicity important for the AST? - Week 4 - Lecture 8 | -- | 5:44 | Free | View in iTunes |

170 | Why are alternating series important? - Week 4 - Lecture 9 | -- | 6:09 | Free | View in iTunes |

171 | Why is e irrational? - Week 4 - Lecture 10 | -- | 8:41 | Free | View in iTunes |

172 | Alternating Series: What is the limit comparison test? | -- | -- | Free | View in iTunes |

173 | When do two series share the same fate? - Week 4 - Lecture 11 | -- | 5:53 | Free | View in iTunes |

174 | Alternating Series: How is convergence affected by the choice of initial index? | -- | -- | Free | View in iTunes |

175 | Why can people get away with writing ∑ₙ aₙ? - Week 4 - Lecture 12 | -- | 4:31 | Free | View in iTunes |

176 | Why is this all so vague… or coarse? - Week 4 - Lecture 13 | -- | 6:06 | Free | View in iTunes |

177 | What happens when I rearrange the terms in a series? - Week 4 - Lecture 14 | -- | 7:19 | Free | View in iTunes |

178 | Alternating Series: By the end of the week... | -- | -- | Free | View in iTunes |

179 | Power Series: Week 5 - Power Series | -- | -- | Free | View in iTunes |

180 | What are power series? - Week 5 Introduction | -- | 3:04 | Free | View in iTunes |

181 | Power Series: Where does a power series converge? | -- | -- | Free | View in iTunes |

182 | For which values does a power series converge? - Week 5 - Lecture 1 | -- | 3:48 | Free | View in iTunes |

183 | Why does a power series converge absolutely? - Week 5 - Lecture 2 | -- | 4:53 | Free | View in iTunes |

184 | How complicated might the interval of convergence be? - Week 5 - Lecture 3 | -- | 5:15 | Free | View in iTunes |

185 | Power Series: What is the radius of convergence? | -- | -- | Free | View in iTunes |

186 | How do I find the radius of convergence? - Week 5 - Lecture 4 | -- | 3:26 | Free | View in iTunes |

187 | What if the radius of convergence is infinity? - Week 5 - Lecture 5 | -- | 4:03 | Free | View in iTunes |

188 | What if the radius of convergence is zero? - Week 5 - Lecture 6 | -- | 3:26 | Free | View in iTunes |

189 | Power Series: What if I'd like a power series in terms of (x-c)? | -- | -- | Free | View in iTunes |

190 | What is a power series centered around a? - Week 5 - Lecture 7 | -- | 4:07 | Free | View in iTunes |

191 | Power Series: Can I do calculus with power series? | -- | -- | Free | View in iTunes |

192 | Can I differentiate a power series? - Week 5 - Lecture 8 | -- | 3:31 | Free | View in iTunes |

193 | Can I integrate a power series? - Week 5 - Lecture 9 | -- | 6:18 | Free | View in iTunes |

194 | Why might I believe that ∑ (xⁿ)/(n!) is eˣ? - Week 5 - Lecture 10 | -- | 4:14 | Free | View in iTunes |

195 | What happens if I multiply two power series? - Week 5 - Lecture 11 | -- | 9:28 | Free | View in iTunes |

196 | What happens if I transform 1/(1-x)? - Week 5 - Lecture 12 | -- | 6:59 | Free | View in iTunes |

197 | Power Series: What is a formula for the Fibonacci numbers? | -- | -- | Free | View in iTunes |

198 | What is a formula for the Fibonacci numbers? - Week 5 - Lecture 13 | -- | 12:12 | Free | View in iTunes |

199 | Power Series: By the end of the week... | -- | -- | Free | View in iTunes |

200 | Taylor Series: Week 6 - Taylor Series | -- | -- | Free | View in iTunes |

201 | What is this last week about? - Week 6 Introduction | -- | 2:11 | Free | View in iTunes |

202 | Taylor Series: What are Taylor series? | -- | -- | Free | View in iTunes |

203 | What is better than a linear approximation? - Week 6 - Lecture 1 | -- | 14:12 | Free | View in iTunes |

204 | What is the Taylor series of f around zero? - Week 6 - Lecture 2 | -- | 10:12 | Free | View in iTunes |

205 | What is the Taylor series of f centered around a? - Week 6 - Lecture 3 | -- | 4:39 | Free | View in iTunes |

206 | What is the Taylor series for sin x around zero? - Week 6 - Lecture 4 | -- | 4:36 | Free | View in iTunes |

207 | Taylor Series: What is Taylor's theorem? | -- | -- | Free | View in iTunes |

208 | What is Taylor's theorem? - Week 6 - Lecture 5 | -- | 11:42 | Free | View in iTunes |

209 | Why is the radius of convergence of 1/(1+x²) so small? - Week 6 - Lecture 6 | -- | 9:52 | Free | View in iTunes |

210 | How is Taylor's theorem like the mean value theorem? - Week 6 - Lecture 7 | -- | 8:04 | Free | View in iTunes |

211 | Taylor Series: What can I do with this, in practice? | -- | -- | Free | View in iTunes |

212 | Approximately, what is cos x when x is near zero? - Week 6 - Lecture 8 | -- | 8:15 | Free | View in iTunes |

213 | How do Taylor series provide intuition for limits? - Week 6 - Lecture 9 | -- | 11:04 | Free | View in iTunes |

214 | Taylor Series: What can I do with this, in theory? | -- | -- | Free | View in iTunes |

215 | What is a real analytic function? - Week 6 - Lecture 10 | -- | 4:54 | Free | View in iTunes |

216 | How are real analytic functions like holograms? - Week 6 - Lecture 11 | -- | 4:24 | Free | View in iTunes |

217 | Taylor Series: By the end of the week | -- | -- | Free | View in iTunes |

218 | Farewell | -- | -- | Free | View in iTunes |

218 Items |

#### Customer Reviews

##### Simply great for the already math inclined

This course is terrific for those already mathematically inclined. The professor has a fun attitude, the visuals are extremely helpful (and sometimes sophisticated), and the content can, for the most part, be followed easily and logically from one step to the next. As someone who has taken advanced mathematics courses which brush up against the subject of sequences, this course has greatly filled in some foundational gaps.

Thanks so much to the author/presenter.