Question

Convergence of geometric series with |r|>1

score 11.3k · Answer 1 · 2026-04-11 01:54:12

11.3k

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Convergence of geometric series with |r|>1

Published on 11 Apr 2026 - 1:54

score 334 · Answer 2 · 2026-04-11 07:26:35

334

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Analytic Expression for special integral

Published on 11 Apr 2026 - 7:26

score 46 · Answer 3 · 2026-04-15 21:29:21

46

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Why is it true that $\sum_{\sigma \in S(n)} a_{\sigma(1)}a_{\sigma(2)} = 2(n-2)! \sum_{1\le i<j \le n}a_ja_k$?

Published on 15 Apr 2026 - 21:29

score 105 · Answer 4 · 2026-04-11 19:15:17

105

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Integers between $00$ and $99$ Inclusive occur as the last two digits in the decimal expansion of infinitely many $a_i$

Published on 11 Apr 2026 - 19:15

score 996 · Answer 5 · 2026-04-15 13:39:49

996

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Prove by induction that $2^n\le (n+1)!$ for all $n\in\Bbb N$.

Published on 15 Apr 2026 - 13:39

score 173 · Answer 6 · 2026-04-17 03:46:08

173

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Prove that $ \liminf_{t\to+\infty} f'(t)\leq 0 \leq \limsup_{t\to+\infty} f'(t) $

Published on 17 Apr 2026 - 3:46

score 67 · Answer 7 · 2026-04-16 23:09:44

$n,m$ are natural positive integers. F$(n,1)$=F$(1,n)=1$ F$(n,m+1)$+F$(n+1,m)=$F$(n+1,m+1)$ Write F($2,n$) and F($3,n$) as a function of $n$

score 882 · Answer 8 · 2026-04-09 05:48:27

882

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How can we convert double sums to single sums?

Published on 09 Apr 2026 - 5:48

score 145 · Answer 9 · 2026-04-13 19:00:54

145

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A particular non-telescoping infinite sum

Published on 13 Apr 2026 - 19:00

score 94 · Answer 10 · 2026-04-16 10:58:13

94

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Using circles to map $\mathbb{N}\to \mathbb{N^2}$

Published on 16 Apr 2026 - 10:58

score 160 · Answer 11 · 2026-04-17 13:02:32

160

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Assessing Whether the Series $\sum_\limits{n = 0}^\infty (-1)^n x^{2n} = 1 - x^2 + x^4 - x^6 + \dots$ Converges (conditional/absolute) or Diverges?

Published on 17 Apr 2026 - 13:02

score 55 · Answer 12 · 2026-04-12 02:34:39

55

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How to prove infinite product converging to sin and cos?

Published on 12 Apr 2026 - 2:34

score 2.1k · Answer 13 · 2026-04-15 22:29:18

2.1k

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If the series $\sum n a_n$ is convergent, then $\sum a_n$ converges to zero?

Published on 15 Apr 2026 - 22:29

score 92 · Answer 14 · 2026-04-11 13:24:55

92

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Sequence of subspaces is dense. Limit of Operator norm

Published on 11 Apr 2026 - 13:24

score 155 · Answer 15 · 2026-04-14 14:54:35

155

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What is the sign and exact value of this sum: $\sum_{n=0}^{+\infty}(-1)^n \tan(\frac{1}{n!})$?

Published on 14 Apr 2026 - 14:54

List Question

Convergence of geometric series with |r|>1

Analytic Expression for special integral

Why is it true that $\sum_{\sigma \in S(n)} a_{\sigma(1)}a_{\sigma(2)} = 2(n-2)! \sum_{1\le i<j \le n}a_ja_k$?

Integers between $00$ and $99$ Inclusive occur as the last two digits in the decimal expansion of infinitely many $a_i$

Prove by induction that $2^n\le (n+1)!$ for all $n\in\Bbb N$.

Prove that $ \liminf_{t\to+\infty} f'(t)\leq 0 \leq \limsup_{t\to+\infty} f'(t) $

$n,m$ are natural positive integers. F$(n,1)$=F$(1,n)=1$ F$(n,m+1)$+F$(n+1,m)=$F$(n+1,m+1)$ Write F($2,n$) and F($3,n$) as a function of $n$

How can we convert double sums to single sums?

A particular non-telescoping infinite sum

Using circles to map $\mathbb{N}\to \mathbb{N^2}$

Assessing Whether the Series $\sum_\limits{n = 0}^\infty (-1)^n x^{2n} = 1 - x^2 + x^4 - x^6 + \dots$ Converges (conditional/absolute) or Diverges?

How to prove infinite product converging to sin and cos?

If the series $\sum n a_n$ is convergent, then $\sum a_n$ converges to zero?

Sequence of subspaces is dense. Limit of Operator norm

What is the sign and exact value of this sum: $\sum_{n=0}^{+\infty}(-1)^n \tan(\frac{1}{n!})$?

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