Question

Euler's "On transcendental progressions..." [E19]

score 118 · Answer 1 · 2026-04-08 23:08:57

118

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Euler's "On transcendental progressions..." [E19]

Published on 08 Apr 2026 - 23:08

score 1.3k · Answer 2 · 2026-03-27 08:16:30

1.3k

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Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Published on 27 Mar 2026 - 8:16

score 883 · Answer 3 · 2026-03-29 14:59:22

883

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Prove that if $\lim_{n \to \infty} f(x_n) = f(\lim_{n \to \infty} x_n)$ for all sequences that converge to $x$, then $f$ is continuous

Published on 29 Mar 2026 - 14:59

score 141 · Answer 4 · 2026-03-29 18:33:26

141

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Is it known how to evaluate $\int_0^1\frac{(1-x)x^{n+1}}{\sin (\pi x)}dx$, for integers $n\geq 1$?

Published on 29 Mar 2026 - 18:33

score 174 · Answer 5 · 2026-04-11 20:11:38

174

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Is this a sufficient condition for the existence of a limit?

Published on 11 Apr 2026 - 20:11

score 124 · Answer 6 · 2018-01-31 21:28:33

124

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Prove that the series $\sum_{n=1}^{\infty}\frac{1}{(n+x)(n+x+1)(n+x+2)}$ has a sum of $\frac{1}{2(x+1)(x+2)}$

Published on 31 Jan 2018 - 21:28

score 49 · Answer 7 · 2018-01-31 21:44:58

49

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For which value of $x \in R $ the following series converges $ \sum_{n=1}^\infty\frac{(x)^{n}}{(2+x)^n}$

Published on 31 Jan 2018 - 21:44

score 120 · Answer 8 · 2018-01-31 22:02:20

120

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Compute $\sum\limits_{n=1}^{\infty}\frac{\cos n}{2^n}$

Published on 31 Jan 2018 - 22:02

score 64 · Answer 9 · 2026-04-12 02:01:45

64

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Relation between sequence and sums

Published on 12 Apr 2026 - 2:01

score 43 · Answer 10 · 2026-03-25 01:18:21

43

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Riemann rearrangement of series applies here?

Published on 25 Mar 2026 - 1:18

score 437 · Answer 11 · 2026-04-06 22:37:10

437

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Prove $\sum_{n=1}^\infty \text{Ci}(\pi n)=\frac{\ln(2)-\gamma}{2}$

Published on 06 Apr 2026 - 22:37

score 157 · Answer 12 · 2018-02-01 02:27:35

157

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Double sequence convergent iff all of its subsequence converge?

Published on 01 Feb 2018 - 2:27

score 65 · Answer 13 · 2018-02-01 02:54:12

65

Views

Why do I get a contradiction for this proof a sequence is decreasing?

Published on 01 Feb 2018 - 2:54

score 128 · Answer 14 · 2026-03-25 03:00:33

128

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convergence of $\sqrt{-e-e²+e^3+\frac{1}{-e-e²+e^3}-\frac{1}{\sqrt{-e-e²+e^3}}+\frac{1}{\sqrt[3]{-e-e²+e^3}}-\frac{1}{\sqrt[5]{-e-e²+e^3}}+\cdots }$?

Published on 25 Mar 2026 - 3:00

score 69 · Answer 15 · 2026-04-12 06:24:09

69

Views

Sum of infinite series pls

Published on 12 Apr 2026 - 6:24

List Question

Euler's "On transcendental progressions..." [E19]

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Prove that if $\lim_{n \to \infty} f(x_n) = f(\lim_{n \to \infty} x_n)$ for all sequences that converge to $x$, then $f$ is continuous

Is it known how to evaluate $\int_0^1\frac{(1-x)x^{n+1}}{\sin (\pi x)}dx$, for integers $n\geq 1$?

Is this a sufficient condition for the existence of a limit?

Prove that the series $\sum_{n=1}^{\infty}\frac{1}{(n+x)(n+x+1)(n+x+2)}$ has a sum of $\frac{1}{2(x+1)(x+2)}$

For which value of $x \in R $ the following series converges $ \sum_{n=1}^\infty\frac{(x)^{n}}{(2+x)^n}$

Compute $\sum\limits_{n=1}^{\infty}\frac{\cos n}{2^n}$

Relation between sequence and sums

Riemann rearrangement of series applies here?

Prove $\sum_{n=1}^\infty \text{Ci}(\pi n)=\frac{\ln(2)-\gamma}{2}$

Double sequence convergent iff all of its subsequence converge?

Why do I get a contradiction for this proof a sequence is decreasing?

convergence of $\sqrt{-e-e²+e^3+\frac{1}{-e-e²+e^3}-\frac{1}{\sqrt{-e-e²+e^3}}+\frac{1}{\sqrt[3]{-e-e²+e^3}}-\frac{1}{\sqrt[5]{-e-e²+e^3}}+\cdots }$?

Sum of infinite series pls

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