Question

Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$

score 751 · Answer 1 · 2026-03-25 04:41:00

751

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Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$

Published on 25 Mar 2026 - 4:41

score 34 · Answer 2 · 2019-09-06 02:25:31

34

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Can convergence interval of series differ by representation?

Published on 06 Sep 2019 - 2:25

score 80 · Answer 3 · 2019-09-06 14:02:37

80

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If $\lim_{x \to R} \sum_{n = 0}^{\infty} a_n x^n = c \in \mathbb{R}$, does $\sum_{n = 0}^{\infty} a_n R^n$ converge?

Published on 06 Sep 2019 - 14:02

score 100 · Answer 4 · 2019-09-06 16:13:18

100

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Radius of convergence of the series $\displaystyle\sum_{n=0}^{\infty}n!z^{2n+1}$

Published on 06 Sep 2019 - 16:13

score 61 · Answer 5 · 2026-04-03 01:04:41

61

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Is there a $C^{\infty}$ function $f$ such that the radius of convergence of $\sum_{n=0}^\infty \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n$ is $0$?

Published on 03 Apr 2026 - 1:04

score 310 · Answer 6 · 2019-09-09 14:28:13

310

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radius of convergence of $\dfrac{1}{1-x}$

Published on 09 Sep 2019 - 14:28

score 233 · Answer 7 · 2019-09-10 04:29:14

233

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proving radius of convergence for power series

Published on 10 Sep 2019 - 4:29

score 152 · Answer 8 · 2019-09-10 15:43:58

152

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Differentiable power series - check my proof

Published on 10 Sep 2019 - 15:43

score 85 · Answer 9 · 2019-09-11 02:07:19

85

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Proving $\sum_{k=0}^\infty x^kk^n/k!=(x\, \mathrm d/\mathrm dx)^n e^x$

Published on 11 Sep 2019 - 2:07

score 182 · Answer 10 · 2026-03-29 18:33:25

182

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Is there a general formula to prove the equivalency of these two expansions of $~\dfrac{1}{(1-x)^2}~$?

Published on 29 Mar 2026 - 18:33

score 58 · Answer 11 · 2019-09-12 04:21:21

58

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Prove that radius of convergence of a new series is no less that the old one

Published on 12 Sep 2019 - 4:21

score 81 · Answer 12 · 2019-09-13 04:32:36

81

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Power of a convergent series

Published on 13 Sep 2019 - 4:32

score 669 · Answer 13 · 2026-03-28 15:21:12

669

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Find the taylor series at $z=3$ of $f(z)=\frac{z(z-3)}{(z-1)}$

Published on 28 Mar 2026 - 15:21

score 181 · Answer 14 · 2026-04-03 17:32:40

181

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Prove that if analytic function $f$ is such $f(0) \neq 0$, it has no zeroes in a certain disk

Published on 03 Apr 2026 - 17:32

score 71 · Answer 15 · 2019-09-13 08:46:19

71

Views

the calculation of a power series

Published on 13 Sep 2019 - 8:46

List Question

Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$

Can convergence interval of series differ by representation?

If $\lim_{x \to R} \sum_{n = 0}^{\infty} a_n x^n = c \in \mathbb{R}$, does $\sum_{n = 0}^{\infty} a_n R^n$ converge?

Radius of convergence of the series $\displaystyle\sum_{n=0}^{\infty}n!z^{2n+1}$

Is there a $C^{\infty}$ function $f$ such that the radius of convergence of $\sum_{n=0}^\infty \frac{f^{(n)}(x_0)}{n!} (x-x_0)^n$ is $0$?

radius of convergence of $\dfrac{1}{1-x}$

proving radius of convergence for power series

Differentiable power series - check my proof

Proving $\sum_{k=0}^\infty x^kk^n/k!=(x\, \mathrm d/\mathrm dx)^n e^x$

Is there a general formula to prove the equivalency of these two expansions of $~\dfrac{1}{(1-x)^2}~$?

Prove that radius of convergence of a new series is no less that the old one

Power of a convergent series

Find the taylor series at $z=3$ of $f(z)=\frac{z(z-3)}{(z-1)}$

Prove that if analytic function $f$ is such $f(0) \neq 0$, it has no zeroes in a certain disk

the calculation of a power series

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