Question

How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?

score 186 · Answer 1 · 2014-11-19 13:43:05

186

Views

How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?

Published on 19 Nov 2014 - 13:43

score 113 · Answer 2 · 2014-11-19 19:19:43

113

Views

Find power series expansion and radius of convergence

Published on 19 Nov 2014 - 19:19

score 90 · Answer 3 · 2026-04-01 14:27:55

90

Views

Power Series: Derivative

Published on 01 Apr 2026 - 14:27

score 146 · Answer 4 · 2026-03-28 16:56:54

146

Views

Estimating integral $\int_0^{0.5} \ln(1+\frac{x^2}{4})$

Published on 28 Mar 2026 - 16:56

score 113 · Answer 5 · 2026-03-26 19:20:11

113

Views

Large-z limit of the other second derivative of the Laguerre polynomial

Published on 26 Mar 2026 - 19:20

score 2.3k · Answer 6 · 2014-11-21 03:04:02

2.3k

Views

Solving the ODE $y''-2x^2y'+4xy=x^2+2x+2$ using power series

Published on 21 Nov 2014 - 3:04

score 64 · Answer 7 · 2026-04-05 21:30:24

64

Views

Coefficeient of $x^k$ in $(1+x)^n$ when $n<0$

Published on 05 Apr 2026 - 21:30

score 79 · Answer 8 · 2014-11-21 20:21:46

79

Views

Find all complex $z$ such that $\sum_{n=1}^{\infty} \frac{e^{nz^2}}{n}$ is convergent

Published on 21 Nov 2014 - 20:21

score 70 · Answer 9 · 2014-11-22 13:18:12

70

Views

Maclaurin series construction

Published on 22 Nov 2014 - 13:18

score 42 · Answer 10 · 2014-11-22 21:10:13

42

Views

Formal power series question

Published on 22 Nov 2014 - 21:10

score 134 · Answer 11 · 2014-11-22 22:10:15

134

Views

Sum of Series - Intelligent Manipulation

Published on 22 Nov 2014 - 22:10

score 270 · Answer 12 · 2014-11-23 04:51:41

270

Views

the first $2k$ terms of the power series of $\sec x + \tan x$ at $x=-\pi/2$

Published on 23 Nov 2014 - 4:51

score 78 · Answer 13 · 2014-11-23 14:53:38

78

Views

If $x_k ≥ 0\;\forall \in \mathbb N$, and $y_k$ a bounded sequence, then the series $\sum_{k=1}^\infty x_ky_k$ converges

Published on 23 Nov 2014 - 14:53

score 208 · Answer 14 · 2026-03-28 00:50:20

208

Views

Laurent Series Expansion for $f(z)=\dfrac{z+2}{(z+1)(z-2)}$ in $\{1<|z|<2\}$ and $\{2<|z|<\infty\}$

Published on 28 Mar 2026 - 0:50

score 38 · Answer 15 · 2014-11-24 17:37:54

38

Views

Where the power series is convergent

Published on 24 Nov 2014 - 17:37

List Question

How do I express the sum $(1+k)+(1+k)^2+\ldots+(1+k)^N$ for $|k|\ll1$ as a series?

Find power series expansion and radius of convergence

Power Series: Derivative

Estimating integral $\int_0^{0.5} \ln(1+\frac{x^2}{4})$

Large-z limit of the other second derivative of the Laguerre polynomial

Solving the ODE $y''-2x^2y'+4xy=x^2+2x+2$ using power series

Coefficeient of $x^k$ in $(1+x)^n$ when $n<0$

Find all complex $z$ such that $\sum_{n=1}^{\infty} \frac{e^{nz^2}}{n}$ is convergent

Maclaurin series construction

Formal power series question

Sum of Series - Intelligent Manipulation

the first $2k$ terms of the power series of $\sec x + \tan x$ at $x=-\pi/2$

If $x_k ≥ 0\;\forall \in \mathbb N$, and $y_k$ a bounded sequence, then the series $\sum_{k=1}^\infty x_ky_k$ converges

Laurent Series Expansion for $f(z)=\dfrac{z+2}{(z+1)(z-2)}$ in $\{1<|z|<2\}$ and $\{2<|z|<\infty\}$

Where the power series is convergent

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