Question

Check simple proof that $\lim\limits_{s\to0^+}\sum\limits_{n=1}^\infty(-1)^nf(n)^{-s}=-\frac12$ if $f>0$, $f''\le0$ and $f(+\infty)=+\infty$

score 367 · Answer 1 · 2026-04-17 00:23:05

367

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Check simple proof that $\lim\limits_{s\to0^+}\sum\limits_{n=1}^\infty(-1)^nf(n)^{-s}=-\frac12$ if $f>0$, $f''\le0$ and $f(+\infty)=+\infty$

Published on 17 Apr 2026 - 0:23

score 393 · Answer 2 · 2026-04-13 19:57:06

393

Views

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score 124 · Answer 5 · 2026-05-15 15:08:36

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score 28 · Answer 6 · 2026-04-13 09:55:28

28

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score 351 · Answer 7 · 2026-04-14 12:01:34

351

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score 50 · Answer 8 · 2026-04-15 09:07:57

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score 147 · Answer 9 · 2026-04-11 17:30:34

147

Views

How would I go about solving $\sum_{j=1}^\infty\sum_{k=1}^\infty \frac{1}{j^2(j+k)^2}$?

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score 223 · Answer 10 · 2026-04-13 06:05:18

223

Views

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47

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score 305 · Answer 12 · 2026-04-14 06:41:22

305

Views

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score 233 · Answer 13 · 2026-04-16 08:38:24

233

Views

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Published on 16 Apr 2026 - 8:38

score 42 · Answer 14 · 2026-05-11 03:27:09

42

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score 91 · Answer 15 · 2026-05-05 16:41:58

91

Views

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Published on 05 May 2026 - 16:41

List Question

Check simple proof that $\lim\limits_{s\to0^+}\sum\limits_{n=1}^\infty(-1)^nf(n)^{-s}=-\frac12$ if $f>0$, $f''\le0$ and $f(+\infty)=+\infty$

Sum of identically distributed but not independent Bernoulli's is non-uniform

Definite Integral of an Infinite Sum

Gamma and incomplete gamma functions- when are they equal?

$(X,d)$ is compact if each $(X,d_k)$ is compact

Question regarding the frequency a sequence takes specific values

Book recommendation - The Fibonacci Sequence and the Golden Ratio

Bit-length function that returns msb '1' and lsb '1'

How would I go about solving $\sum_{j=1}^\infty\sum_{k=1}^\infty \frac{1}{j^2(j+k)^2}$?

Sum and Product combined infinite sequence

Show that $u_n$ > $\sqrt{3}$

Can the infinite sum of $\frac{2^{2k-1}}{5^{k+3}}$ be calculated with the formula of geometric series?

Calculate $\sum_{n=0}^\infty \frac1{(4n^2 - 1)^2}$

A sequence of numbers easily computable with no apparent order and with defined inverse function

Finding the $n$-th derivative from $e^{x^{40}}$ using Maclaurin series

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