Question

A conjecture regarding a strange infinite sum

score 96 · Answer 1 · 2026-04-16 02:25:56

96

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A conjecture regarding a strange infinite sum

Published on 16 Apr 2026 - 2:25

score 134 · Answer 2 · 2026-04-15 19:57:01

134

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To Evaluate the Limit $\lim_{n \to \infty}\left(1+\sum_{k=1}^{n} \frac{1}{\binom{n}{k}}\right)^n$

Published on 15 Apr 2026 - 19:57

score 80 · Answer 3 · 2026-04-17 11:59:03

80

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Evaluate $\,\lim_{n\to\infty}\frac{n^2}{({n^2+1^2})^{3/2}} + \frac{n^2}{({n^2+3^2})^{3/2}} + \cdots + \frac{n^2}{({n^2+(n-1)^2})^{3/2}}$

Published on 17 Apr 2026 - 11:59

score 51 · Answer 4 · 2026-04-09 23:22:22

51

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Formula to calculate sum of amount at 7% rate to 10th term.

Published on 09 Apr 2026 - 23:22

score 51 · Answer 5 · 2026-04-09 10:04:31

51

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Given f such that $ f(0)=0, \lim_{x\to \infty} f(x) = 1$, is $f_n(x)=f(x+e^n)$ uniformly convergent?

Published on 09 Apr 2026 - 10:04

score 911 · Answer 6 · 2026-04-09 03:15:56

911

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General term of a sequence.

Published on 09 Apr 2026 - 3:15

score 84 · Answer 7 · 2026-04-13 10:53:00

84

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$\lim_{n \to \infty}\sum_{r=1}^{n}\frac{r^2}{n^3 + n^2 + r}$

Published on 13 Apr 2026 - 10:53

score 175 · Answer 8 · 2026-04-29 15:27:57

175

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Shifted sum of reciprocals of primes: $\sum \limits_{\forall p \in primes}\frac{1}{p+1}$

Published on 29 Apr 2026 - 15:27

score 2.2k · Answer 9 · 2026-04-16 03:12:35

2.2k

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Show that $\sum_{k=0}^n (k+1)x^k = \sum_{k=1}^{n+1} (k)x^{k+1}$.

Published on 16 Apr 2026 - 3:12

score 185 · Answer 10 · 2026-04-12 06:14:53

185

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Simplifying an infinite fraction

Published on 12 Apr 2026 - 6:14

score 34 · Answer 11 · 2026-04-09 10:08:07

34

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Is $\sum_{j=0}^\infty \frac{x}{(1+x^2)^j}$ pointwise convergent or uniform convergent?

Published on 09 Apr 2026 - 10:08

score 125 · Answer 12 · 2026-04-10 15:18:15

125

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basic sequences question

Published on 10 Apr 2026 - 15:18

score 134 · Answer 13 · 2026-04-15 10:33:54

134

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Use any method, determine whether the series $\sum_{k=1}^{\infty} \frac{7^{k} + k}{k! + 1}$ converges?

Published on 15 Apr 2026 - 10:33

score 445 · Answer 14 · 2026-04-13 23:43:04

445

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Why does the following Maclaurin series equal this catenary curve?

Published on 13 Apr 2026 - 23:43

score 163 · Answer 15 · 2026-04-13 01:51:42

163

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On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Published on 13 Apr 2026 - 1:51

List Question

A conjecture regarding a strange infinite sum

To Evaluate the Limit $\lim_{n \to \infty}\left(1+\sum_{k=1}^{n} \frac{1}{\binom{n}{k}}\right)^n$

Evaluate $\,\lim_{n\to\infty}\frac{n^2}{({n^2+1^2})^{3/2}} + \frac{n^2}{({n^2+3^2})^{3/2}} + \cdots + \frac{n^2}{({n^2+(n-1)^2})^{3/2}}$

Formula to calculate sum of amount at 7% rate to 10th term.

Given f such that $ f(0)=0, \lim_{x\to \infty} f(x) = 1$, is $f_n(x)=f(x+e^n)$ uniformly convergent?

General term of a sequence.

$\lim_{n \to \infty}\sum_{r=1}^{n}\frac{r^2}{n^3 + n^2 + r}$

Shifted sum of reciprocals of primes: $\sum \limits_{\forall p \in primes}\frac{1}{p+1}$

Show that $\sum_{k=0}^n (k+1)x^k = \sum_{k=1}^{n+1} (k)x^{k+1}$.

Simplifying an infinite fraction

Is $\sum_{j=0}^\infty \frac{x}{(1+x^2)^j}$ pointwise convergent or uniform convergent?

basic sequences question

Use any method, determine whether the series $\sum_{k=1}^{\infty} \frac{7^{k} + k}{k! + 1}$ converges?

Why does the following Maclaurin series equal this catenary curve?

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

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