Question

A better closed-form solution to recursive equation

score 58 · Answer 1 · 2026-05-11 05:11:30

58

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A better closed-form solution to recursive equation

Published on 11 May 2026 - 5:11

score 77 · Answer 2 · 2026-04-14 02:46:37

77

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When do there exist two functions that satisfy the equation?

Published on 14 Apr 2026 - 2:46

score 347 · Answer 3 · 2026-04-25 06:47:47

347

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Understanding the proof: If $a_1=1$ and $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}.$ Then, $\lim\limits_{n\to\infty}\frac{a_n}{n}=\frac{1}{2}$

Published on 25 Apr 2026 - 6:47

score 54 · Answer 4 · 2026-04-16 13:51:58

54

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Example for this criterion?

Published on 16 Apr 2026 - 13:51

score 315 · Answer 5 · 2026-05-10 22:04:32

315

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Extended conjecture for $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(\sum\limits_{k = 1 }^\infty \frac{a_k \pi}{b_k}P_k(n) \right)$

Published on 10 May 2026 - 22:04

score 185 · Answer 6 · 2026-05-11 05:00:01

185

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How to apply the central Limit theorem?

Published on 11 May 2026 - 5:00

score 271 · Answer 7 · 2026-04-15 06:41:07

271

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Convergence of the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{x^n}$.

Published on 15 Apr 2026 - 6:41

score 126 · Answer 8 · 2026-04-12 10:30:02

126

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What can I say about the consecutive difference of a convergent sequence?

Published on 12 Apr 2026 - 10:30

score 67 · Answer 9 · 2026-04-17 07:40:21

67

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Prove / disprove if $\lim((a_{n})^2+ (b_{n})^2)=0$ then $\lim(a_{n})=0$ and $\lim(b_{n})=0$

Published on 17 Apr 2026 - 7:40

score 230 · Answer 10 · 2026-04-16 17:31:52

230

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Sum of $\frac{1}{1 \cdot 2} + \frac{1}{3\cdot 4} + \cdots$

Published on 16 Apr 2026 - 17:31

score 167 · Answer 11 · 2026-04-15 18:35:31

167

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Show that $\sum_{n=0}^{\infty} \frac{3^{2n+1}(3n)!}{n!(2n+1)!4^{3n+1}}=1$

Published on 15 Apr 2026 - 18:35

score 265 · Answer 12 · 2026-04-14 15:23:27

265

Views

Find out the subsequential limits of a sequence

Published on 14 Apr 2026 - 15:23

score 259 · Answer 13 · 2026-04-16 11:19:15

259

Views

Let $I_1, I_2, \cdots$ be any countable collection of intervals, whose union contains some interval $I$, then $\sum P(I_j) \geq P(I)$.

Published on 16 Apr 2026 - 11:19

score 544 · Answer 14 · 2026-04-14 04:39:52

544

Views

Calculate common difference and the first term

Published on 14 Apr 2026 - 4:39

score 392 · Answer 15 · 2026-04-11 20:45:03

392

Views

Changing the order of a double sum

Published on 11 Apr 2026 - 20:45

List Question

A better closed-form solution to recursive equation

When do there exist two functions that satisfy the equation?

Understanding the proof: If $a_1=1$ and $a_{n+1}=\sqrt{a_1+a_2+\cdots+a_n}.$ Then, $\lim\limits_{n\to\infty}\frac{a_n}{n}=\frac{1}{2}$

Example for this criterion?

Extended conjecture for $f(m)=\sum\limits_{n = 1 }^ m (-1)^n \sin\left(\sum\limits_{k = 1 }^\infty \frac{a_k \pi}{b_k}P_k(n) \right)$

How to apply the central Limit theorem?

Convergence of the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{x^n}$.

What can I say about the consecutive difference of a convergent sequence?

Prove / disprove if $\lim((a_{n})^2+ (b_{n})^2)=0$ then $\lim(a_{n})=0$ and $\lim(b_{n})=0$

Sum of $\frac{1}{1 \cdot 2} + \frac{1}{3\cdot 4} + \cdots$

Show that $\sum_{n=0}^{\infty} \frac{3^{2n+1}(3n)!}{n!(2n+1)!4^{3n+1}}=1$

Find out the subsequential limits of a sequence

Let $I_1, I_2, \cdots$ be any countable collection of intervals, whose union contains some interval $I$, then $\sum P(I_j) \geq P(I)$.

Calculate common difference and the first term

Changing the order of a double sum

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