Question

Golden Rectangle into Golden Rectangles

score 798 · Answer 1 · 2026-04-20 05:17:37

798

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Golden Rectangle into Golden Rectangles

Published on 20 Apr 2026 - 5:17

score 69 · Answer 2 · 2026-04-15 19:05:56

69

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is $\sum_{m=2}^{\infty}{\left(\sum_{n=2}^{\infty}\frac{1}{n^m}\right)}$ divergent or convergent

Published on 15 Apr 2026 - 19:05

score 947 · Answer 3 · 2026-04-14 14:17:41

947

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How to show $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}=2$?

Published on 14 Apr 2026 - 14:17

score 143 · Answer 4 · 2026-04-14 05:45:01

143

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Series convergence test $\sum_{n=1}^\infty 2^{-n-(-1)^n}$

Published on 14 Apr 2026 - 5:45

score 1.1k · Answer 5 · 2026-04-16 19:13:26

1.1k

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Finding the supremum of the set $A = \left\{\sin({n \pi}/{2})-\frac{1}{\sqrt{n}}: n \in \mathbb{N}\right\}$.

Published on 16 Apr 2026 - 19:13

score 1.5k · Answer 6 · 2026-04-09 18:53:14

1.5k

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Proof Explanation: Convergence implies boundedness

Published on 09 Apr 2026 - 18:53

score 333 · Answer 7 · 2026-03-26 01:06:46

333

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Why do Sylvester numbers, when reduced modulo $864$, form an arithmetic progression $7, 43, 79, 115, 151, 187, 223, \ldots$?

Published on 26 Mar 2026 - 1:06

score 1.8k · Answer 8 · 2026-04-17 13:25:30

1.8k

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Is the sequence $3n$ is bounded? Prove or disprove.

Published on 17 Apr 2026 - 13:25

score 41 · Answer 9 · 2026-04-17 02:44:10

41

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Divergence of the sequence $s_n = n$, i.e., the sequence $1,2,3, \dots n$

Published on 17 Apr 2026 - 2:44

score 2.7k · Answer 10 · 2026-04-15 18:11:10

2.7k

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Is the sequence $\{\frac {(-1)^n}{2n}\}$ convergent? If so, what is the limit?

Published on 15 Apr 2026 - 18:11

score 105 · Answer 11 · 2026-04-17 06:29:42

105

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Find the sum of the series $1+\frac12 z^2+\frac{1\cdot3}{2\cdot4}z^4+....$

Published on 17 Apr 2026 - 6:29

score 195 · Answer 12 · 2026-04-11 02:11:12

195

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Compute $\sum\limits_{k=1}^{9999}\frac1{2\sqrt k+1}$

Published on 11 Apr 2026 - 2:11

score 183 · Answer 13 · 2026-04-14 12:49:57

On the series $\sum \limits_{n=1}^{\infty} \frac{1}{n^2-3n+3}$ and $\sum\limits_{n=-\infty}^{\infty} \frac{1}{n^2-3n+3}$

score 611 · Answer 14 · 2026-04-15 19:03:34

611

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Prove that if $F:[a,b]\to \mathbb{R}$, if $F'$ is continuous, and if $|F'(x)|<1$ on $[a,b]$, then $F$ is a contraction. Does $F$ necessarily have

Published on 15 Apr 2026 - 19:03

score 265 · Answer 15 · 2026-04-16 19:42:13

265

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Alternating series inequalities

Published on 16 Apr 2026 - 19:42

List Question

Golden Rectangle into Golden Rectangles

is $\sum_{m=2}^{\infty}{\left(\sum_{n=2}^{\infty}\frac{1}{n^m}\right)}$ divergent or convergent

How to show $\sum_{n=1}^{\infty}\frac{H_{n+1}}{n(n+1)}=2$?

Series convergence test $\sum_{n=1}^\infty 2^{-n-(-1)^n}$

Finding the supremum of the set $A = \left\{\sin({n \pi}/{2})-\frac{1}{\sqrt{n}}: n \in \mathbb{N}\right\}$.

Proof Explanation: Convergence implies boundedness

Why do Sylvester numbers, when reduced modulo $864$, form an arithmetic progression $7, 43, 79, 115, 151, 187, 223, \ldots$?

Is the sequence $3n$ is bounded? Prove or disprove.

Divergence of the sequence $s_n = n$, i.e., the sequence $1,2,3, \dots n$

Is the sequence $\{\frac {(-1)^n}{2n}\}$ convergent? If so, what is the limit?

Find the sum of the series $1+\frac12 z^2+\frac{1\cdot3}{2\cdot4}z^4+....$

Compute $\sum\limits_{k=1}^{9999}\frac1{2\sqrt k+1}$

On the series $\sum \limits_{n=1}^{\infty} \frac{1}{n^2-3n+3}$ and $\sum\limits_{n=-\infty}^{\infty} \frac{1}{n^2-3n+3}$

Prove that if $F:[a,b]\to \mathbb{R}$, if $F'$ is continuous, and if $|F'(x)|<1$ on $[a,b]$, then $F$ is a contraction. Does $F$ necessarily have

Alternating series inequalities

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