Question

Convergence of $\sum_n a_n$ where $0\leq a_{n+1}\leq a_n(1-\beta a_n^{\alpha})$

score 88 · Answer 1 · 2026-04-17 00:26:43

88

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Convergence of $\sum_n a_n$ where $0\leq a_{n+1}\leq a_n(1-\beta a_n^{\alpha})$

Published on 17 Apr 2026 - 0:26

score 250 · Answer 2 · 2026-04-11 21:07:13

250

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Non-recursive formula for discrete function that follows a recursive pattern

Published on 11 Apr 2026 - 21:07

score 43 · Answer 3 · 2026-04-12 15:27:58

43

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Help finding a concise way to express this sequence of integers

Published on 12 Apr 2026 - 15:27

score 452 · Answer 4 · 2026-04-16 15:54:11

452

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If $L$ is a lower bound of $S$, then $L=\inf(S)$ iff $\exists$ a sequence $\{S_n\}$ of elements of $S$ that converges to $L$

Published on 16 Apr 2026 - 15:54

score 1.2k · Answer 5 · 2026-04-13 11:43:24

1.2k

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Infinite sum of $nk^n$

Published on 13 Apr 2026 - 11:43

score 102 · Answer 6 · 2026-04-14 00:08:05

102

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Does $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}i^{n(n+1)}$ converge?

Published on 14 Apr 2026 - 0:08

score 119 · Answer 7 · 2026-04-15 22:48:12

119

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Proving that $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{4n^{2}-1}=\frac{\pi -2}{4}$

Published on 15 Apr 2026 - 22:48

score 50 · Answer 8 · 2026-04-11 21:30:46

50

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Evaluating limit of sequence from $\epsilon$ definition

Published on 11 Apr 2026 - 21:30

score 1.4k · Answer 9 · 2026-05-15 22:17:38

1.4k

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Let a be a real number and let $S = \{ x \in Q : x <a \}.$ prove that $a = sup S.$

Published on 15 May 2026 - 22:17

score 126 · Answer 10 · 2026-04-16 01:38:50

126

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Convergence of the power series $\sum_{n=1}^\infty\frac{(1+n)^n}{n!}x^n $

Published on 16 Apr 2026 - 1:38

score 158 · Answer 11 · 2026-04-15 20:13:34

158

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Prove continuity from preservation of sequential limits but do not use $f(\bar{A}) \subseteq \overline{f(A)}$

Published on 15 Apr 2026 - 20:13

score 113 · Answer 12 · 2026-04-17 17:42:00

Prove that , for every $c \in R$, there exists ${a_{n}}$ of rationals and ${b_{n}}$ of irrationals such that $\lim a_{n} = \lim b_{n} = c$.

score 42 · Answer 13 · 2026-04-11 14:53:57

42

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Finding values for convergence

Published on 11 Apr 2026 - 14:53

score 89 · Answer 14 · 2026-04-16 09:09:33

89

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Use the definition of convergence of a sequence to show the sequence $a_n=4(\frac{3}7)^n +9$ converges.

Published on 16 Apr 2026 - 9:09

score 94 · Answer 15 · 2026-05-16 18:08:50

94

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What is $\lim_{x \to \infty} 0^{\frac{1}{x}}$? Is it 0 or 1 or is it an invalid limit?

Published on 16 May 2026 - 18:08

List Question

Convergence of $\sum_n a_n$ where $0\leq a_{n+1}\leq a_n(1-\beta a_n^{\alpha})$

Non-recursive formula for discrete function that follows a recursive pattern

Help finding a concise way to express this sequence of integers

If $L$ is a lower bound of $S$, then $L=\inf(S)$ iff $\exists$ a sequence $\{S_n\}$ of elements of $S$ that converges to $L$

Infinite sum of $nk^n$

Does $\sum_{n=1}^{\infty} \frac{(-1)^n}{n}i^{n(n+1)}$ converge?

Proving that $\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{4n^{2}-1}=\frac{\pi -2}{4}$

Evaluating limit of sequence from $\epsilon$ definition

Let a be a real number and let $S = \{ x \in Q : x <a \}.$ prove that $a = sup S.$

Convergence of the power series $\sum_{n=1}^\infty\frac{(1+n)^n}{n!}x^n $

Prove continuity from preservation of sequential limits but do not use $f(\bar{A}) \subseteq \overline{f(A)}$

Prove that , for every $c \in R$, there exists ${a_{n}}$ of rationals and ${b_{n}}$ of irrationals such that $\lim a_{n} = \lim b_{n} = c$.

Finding values for convergence

Use the definition of convergence of a sequence to show the sequence $a_n=4(\frac{3}7)^n +9$ converges.

What is $\lim_{x \to \infty} 0^{\frac{1}{x}}$? Is it 0 or 1 or is it an invalid limit?

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