Question

Limit of $\prod_{k=1}^n \frac{(k^2)}{(k+1)^2}$

score 52 · Answer 1 · 2026-04-14 10:11:57

52

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Limit of $\prod_{k=1}^n \frac{(k^2)}{(k+1)^2}$

Published on 14 Apr 2026 - 10:11

score 126 · Answer 2 · 2026-04-15 17:32:35

126

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$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$

Published on 15 Apr 2026 - 17:32

score 180 · Answer 3 · 2026-04-23 20:35:01

180

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Does this cubic sequence converge or diverge?

Published on 23 Apr 2026 - 20:35

score 1.1k · Answer 4 · 2026-04-14 10:43:32

1.1k

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Analytic function at a point is analytic in a neighborhood

Published on 14 Apr 2026 - 10:43

score 47 · Answer 5 · 2026-03-25 22:26:49

47

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Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Published on 25 Mar 2026 - 22:26

score 48 · Answer 6 · 2026-04-16 18:36:47

48

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Let $r \in \Bbb R$ be such that $0 < r < 1$. Prove that the series $r^2 + r + r^4 + r^3 + ... + r^{2n} + r^{2n-1} + ...$ converges or diverges.

Published on 16 Apr 2026 - 18:36

score 55 · Answer 7 · 2026-04-13 15:41:41

55

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Bridge Between Series and Set Theory

Published on 13 Apr 2026 - 15:41

score 95 · Answer 8 · 2026-04-15 02:24:49

95

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Find \lim_{n\to\infty} \sqrt[n]{2n+1}

Published on 15 Apr 2026 - 2:24

score 37 · Answer 9 · 2026-04-13 20:56:43

37

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An alternative term for a function's image, in a limited setting

Published on 13 Apr 2026 - 20:56

score 64 · Answer 10 · 2026-04-16 02:54:43

64

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Laurent series for $f(z)=\frac1{z^3 +1}$ on $0<|z-1|<\sqrt3$

Published on 16 Apr 2026 - 2:54

score 46 · Answer 11 · 2026-04-11 12:01:59

46

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Is it ok to divide this formula by n-1?

Published on 11 Apr 2026 - 12:01

score 50 · Answer 12 · 2026-04-13 15:15:08

50

Views

Recursive sequence problem (while it oscillates)

Published on 13 Apr 2026 - 15:15

score 76 · Answer 13 · 2026-04-17 02:43:49

76

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Prove that $a_{n+1} = 2a_n$ for all integers n≥1. Prove that $a_n = 2^{n−1}$ for n≥1.

Published on 17 Apr 2026 - 2:43

score 164 · Answer 14 · 2026-04-16 08:44:38

164

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Closed form for : $L=1+{1 \over 2^{1/2}}+{1 \over 3^{1/2}}+{1 \over 4^{1/2}}+\cdots$ exist?

Published on 16 Apr 2026 - 8:44

score 123 · Answer 15 · 2026-04-15 07:18:09

123

Views

Sequence $(\frac{a_n}{n})$ is convergent.

Published on 15 Apr 2026 - 7:18

List Question

Limit of $\prod_{k=1}^n \frac{(k^2)}{(k+1)^2}$

$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$

Does this cubic sequence converge or diverge?

Analytic function at a point is analytic in a neighborhood

Show that if $z \in \Bbb C$ is such that $|z| < 1$, then $\sum_{n=0} ^{\infty} {a \choose n}z^n$ converges for any $a \in \Bbb C$.

Let $r \in \Bbb R$ be such that $0 < r < 1$. Prove that the series $r^2 + r + r^4 + r^3 + ... + r^{2n} + r^{2n-1} + ...$ converges or diverges.

Bridge Between Series and Set Theory

Find \lim_{n\to\infty} \sqrt[n]{2n+1}

An alternative term for a function's image, in a limited setting

Laurent series for $f(z)=\frac1{z^3 +1}$ on $0<|z-1|<\sqrt3$

Is it ok to divide this formula by n-1?

Recursive sequence problem (while it oscillates)

Prove that $a_{n+1} = 2a_n$ for all integers n≥1. Prove that $a_n = 2^{n−1}$ for n≥1.

Closed form for : $L=1+{1 \over 2^{1/2}}+{1 \over 3^{1/2}}+{1 \over 4^{1/2}}+\cdots$ exist?

Sequence $(\frac{a_n}{n})$ is convergent.

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