Question

Using a power series to show $\log(2) = \sum_{k = 1}^{\infty} \frac{1}{k \cdot 2^{k}}$

score 86 · Answer 1 · 2026-03-29 10:29:35

86

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Using a power series to show $\log(2) = \sum_{k = 1}^{\infty} \frac{1}{k \cdot 2^{k}}$

Published on 29 Mar 2026 - 10:29

score 2.7k · Answer 2 · 2026-03-29 10:37:17

2.7k

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Finding the Maclaurin series of $e^{\sin x}$ by comparing coefficients

Published on 29 Mar 2026 - 10:37

score 230 · Answer 3 · 2018-11-27 15:27:10

230

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Bounded function with bounded second derivative imply bounded first derivative

Published on 27 Nov 2018 - 15:27

score 28 · Answer 4 · 2026-03-25 08:09:56

28

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Determination of the order of a pole

Published on 25 Mar 2026 - 8:09

score 159 · Answer 5 · 2018-11-28 00:54:31

159

Views

Calucate the coefficient of taylor series

Published on 28 Nov 2018 - 0:54

score 203 · Answer 6 · 2026-03-29 10:37:10

203

Views

Calculate $\sum\limits_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}$

Published on 29 Mar 2026 - 10:37

score 258 · Answer 7 · 2026-03-29 10:37:16

258

Views

Radius of convergence for $\ln(a+x)$

Published on 29 Mar 2026 - 10:37

score 2.7k · Answer 8 · 2018-11-28 20:29:42

2.7k

Views

Find 3rd order Taylor polynomial

Published on 28 Nov 2018 - 20:29

score 83 · Answer 9 · 2018-11-28 22:19:50

83

Views

Simplifying $\sum_{n=0}^{\infty}ne^{-a}\frac{a^{x+n}}{(x+n)!}$, where $x$ is an integer and $a<1$

Published on 28 Nov 2018 - 22:19

score 215 · Answer 10 · 2018-11-29 07:54:08

215

Views

Find the limit of the expression $\lim_{x\to 0}\left(\frac{\sin x}{\arcsin x}\right)^{1/\ln(1+x^2)}$

Published on 29 Nov 2018 - 7:54

score 457 · Answer 11 · 2026-03-29 10:29:38

457

Views

Using the Cauchy-Hadamard Theorem to find a radius of convergence

Published on 29 Mar 2026 - 10:29

score 24 · Answer 12 · 2018-11-29 18:34:26

24

Views

Simplifying $\sum_{n=1}^{x}ne^{-a}\frac{a^{x-n}}{(x-n)!}$, where $x$ is an integer and $a<1$

Published on 29 Nov 2018 - 18:34

score 155 · Answer 13 · 2026-03-25 09:28:27

155

Views

Prove $y^tH_f(a)y \leq 0$ with Taylors Theorem

Published on 25 Mar 2026 - 9:28

score 469 · Answer 14 · 2026-03-29 10:29:32

469

Views

Why does $\sum_{n\geq0}(1-x)^n=\frac1x$ have such a poor radius of convergence?

Published on 29 Mar 2026 - 10:29

score 38 · Answer 15 · 2018-12-01 17:42:52

38

Views

Taylor expansion on Images which are warped

Published on 01 Dec 2018 - 17:42

List Question

Using a power series to show $\log(2) = \sum_{k = 1}^{\infty} \frac{1}{k \cdot 2^{k}}$

Finding the Maclaurin series of $e^{\sin x}$ by comparing coefficients

Bounded function with bounded second derivative imply bounded first derivative

Determination of the order of a pole

Calucate the coefficient of taylor series

Calculate $\sum\limits_{n=0}^{\infty} \frac{x^{3n}}{(3n)!}$

Radius of convergence for $\ln(a+x)$

Find 3rd order Taylor polynomial

Simplifying $\sum_{n=0}^{\infty}ne^{-a}\frac{a^{x+n}}{(x+n)!}$, where $x$ is an integer and $a<1$

Find the limit of the expression $\lim_{x\to 0}\left(\frac{\sin x}{\arcsin x}\right)^{1/\ln(1+x^2)}$

Using the Cauchy-Hadamard Theorem to find a radius of convergence

Simplifying $\sum_{n=1}^{x}ne^{-a}\frac{a^{x-n}}{(x-n)!}$, where $x$ is an integer and $a<1$

Prove $y^tH_f(a)y \leq 0$ with Taylors Theorem

Why does $\sum_{n\geq0}(1-x)^n=\frac1x$ have such a poor radius of convergence?

Taylor expansion on Images which are warped

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