Question

Does $z (s) = \int_0^s \zeta \left( \frac{1}{2} + i t \right) d t = s + \sum_{n = 2}^{\infty} \frac{i (n^{- i s} - 1)}{\ln (n) \sqrt{n}}$ converge?

score 95 · Answer 1 · 2026-05-11 08:42:02

95

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Does $z (s) = \int_0^s \zeta \left( \frac{1}{2} + i t \right) d t = s + \sum_{n = 2}^{\infty} \frac{i (n^{- i s} - 1)}{\ln (n) \sqrt{n}}$ converge?

Published on 11 May 2026 - 8:42

score 136 · Answer 2 · 2026-04-14 14:58:43

136

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Convergence of decreasing decrements of sequences

Published on 14 Apr 2026 - 14:58

score 1.5k · Answer 3 · 2026-04-15 02:06:18

1.5k

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how to prove this limit is zero?

Published on 15 Apr 2026 - 2:06

score 981 · Answer 4 · 2026-05-10 18:19:30

981

Views

Can we solve this recurrence relation?

Published on 10 May 2026 - 18:19

score 71 · Answer 5 · 2026-04-16 03:31:46

71

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Suppose $a_n\geq 0 $ and $ \sum_{n=1}^{\infty}a_n<\infty $. Does it follow that $ a_n=o(1/n) $, as $ n\to \infty $?

Published on 16 Apr 2026 - 3:31

score 388 · Answer 6 · 2026-04-16 18:05:02

388

Views

Finding a general formula for the sequence {$0, 1, 3, 5, 6, 7, 9, 15$}.

Published on 16 Apr 2026 - 18:05

score 262 · Answer 7 · 2026-04-17 11:29:18

262

Views

If $a_n\sim b_n$ decrease to $0$ and $a_{n+1}b_n-a_nb_{n+1}$ changes sign i.o. , does it imply the same for $(1-a_{n+1})(1-b_n)-(1-a_n)(1-b_{n+1})$?

Published on 17 Apr 2026 - 11:29

score 3.9k · Answer 8 · 2026-04-09 03:13:32

3.9k

Views

Formula to find missing numbers in sequence

Published on 09 Apr 2026 - 3:13

score 64 · Answer 9 · 2026-04-14 20:19:40

64

Views

Is $\sum_{m\in \mathbb Z} f(x-m)f(x-n) \in L^2(a,b)$ if $f\in L^2(\mathbb R)$?

Published on 14 Apr 2026 - 20:19

score 849 · Answer 10 · 2026-04-16 04:36:56

849

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Find the formula for the nth term of the sequence and find its limits

Published on 16 Apr 2026 - 4:36

score 178 · Answer 11 · 2026-04-16 00:51:44

178

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Convergence of $\sum_{k=1}^\infty \log(k+1) \frac{e^{\sin(k)}}{e^{k}}$

Published on 16 Apr 2026 - 0:51

score 100 · Answer 12 · 2026-05-05 15:14:53

100

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Proof that the Eulerian Numbers $A(n,m)$ are asymptotic to $(m+1)^n$ when $m$ is fixed and $n\rightarrow\infty$

Published on 05 May 2026 - 15:14

score 1.3k · Answer 13 · 2026-04-15 18:04:57

1.3k

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If $\{x_{n}\}$ is a convergent sequence and $\{y_{n}\}$ is a bounded sequence then what can we say about $\{x_{n}+y_{n}\}$?

Published on 15 Apr 2026 - 18:04

score 387 · Answer 14 · 2026-05-10 22:02:35

387

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Conjecture about $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(P_r(n) \frac{a \pi}{b}\right) $

Published on 10 May 2026 - 22:02

score 175 · Answer 15 · 2026-04-08 17:13:48

175

Views

Limit with terms of convergent series problem

Published on 08 Apr 2026 - 17:13

List Question

Does $z (s) = \int_0^s \zeta \left( \frac{1}{2} + i t \right) d t = s + \sum_{n = 2}^{\infty} \frac{i (n^{- i s} - 1)}{\ln (n) \sqrt{n}}$ converge?

Convergence of decreasing decrements of sequences

how to prove this limit is zero?

Can we solve this recurrence relation?

Suppose $a_n\geq 0 $ and $ \sum_{n=1}^{\infty}a_n<\infty $. Does it follow that $ a_n=o(1/n) $, as $ n\to \infty $?

Finding a general formula for the sequence {$0, 1, 3, 5, 6, 7, 9, 15$}.

If $a_n\sim b_n$ decrease to $0$ and $a_{n+1}b_n-a_nb_{n+1}$ changes sign i.o. , does it imply the same for $(1-a_{n+1})(1-b_n)-(1-a_n)(1-b_{n+1})$?

Formula to find missing numbers in sequence

Is $\sum_{m\in \mathbb Z} f(x-m)f(x-n) \in L^2(a,b)$ if $f\in L^2(\mathbb R)$?

Find the formula for the nth term of the sequence and find its limits

Convergence of $\sum_{k=1}^\infty \log(k+1) \frac{e^{\sin(k)}}{e^{k}}$

Proof that the Eulerian Numbers $A(n,m)$ are asymptotic to $(m+1)^n$ when $m$ is fixed and $n\rightarrow\infty$

If $\{x_{n}\}$ is a convergent sequence and $\{y_{n}\}$ is a bounded sequence then what can we say about $\{x_{n}+y_{n}\}$?

Conjecture about $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(P_r(n) \frac{a \pi}{b}\right) $

Limit with terms of convergent series problem

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