Question

What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?

score 145 · Answer 1 · 2026-04-18 15:09:05

145

Views

What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?

Published on 18 Apr 2026 - 15:09

score 2.6k · Answer 2 · 2026-04-16 20:31:30

Is there a formula for the sequence of numbers 3-6-9-12-15-18-21-24-27-30-36-42-48-54-60-66-72-78-84-90-102-114-126-138-150 etc..?

score 102 · Answer 3 · 2026-04-13 08:33:21

102

Views

Convergence of iteration sequence

Published on 13 Apr 2026 - 8:33

score 868 · Answer 4 · 2026-04-16 22:42:08

868

Views

Divisibility property for sequence $a_{n+2}=-2(n-1)(n+3)a_n-(2n+3)a_{n+1}$

Published on 16 Apr 2026 - 22:42

score 174 · Answer 5 · 2026-04-12 17:46:43

174

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Find $\lim\limits_{n\to\infty}\sum\limits_{k=1}^n \frac{2k+1}{k^2(k+1)^2}$

Published on 12 Apr 2026 - 17:46

score 154 · Answer 6 · 2026-04-16 05:45:15

154

Views

Is the series $\sum_{n=1}^\infty (\sqrt[n]{a}-1)$ convergent or divergent?

Published on 16 Apr 2026 - 5:45

score 239 · Answer 7 · 2026-04-15 18:02:41

239

Views

Prove convergence of alternating sequence with factorial in denominator $\frac{\left(-5\right)^n}{n!}$

Published on 15 Apr 2026 - 18:02

score 2.7k · Answer 8 · 2026-03-25 07:48:38

2.7k

Views

If $a,b,c$ are in $A.P.$ then prove that $b^2>ac$

Published on 25 Mar 2026 - 7:48

score 35 · Answer 9 · 2026-04-13 19:30:08

35

Views

Renyi's proof of Faddeev's theorem: convergence of a series

Published on 13 Apr 2026 - 19:30

score 914 · Answer 10 · 2026-04-14 14:23:24

914

Views

Sum $\sum(2n+1) × 2^n$

Published on 14 Apr 2026 - 14:23

score 189 · Answer 11 · 2026-04-10 03:34:46

189

Views

A problem from Makarov Selected Problems in Real Analysis

Published on 10 Apr 2026 - 3:34

score 278 · Answer 12 · 2026-04-13 17:49:59

278

Views

Why manipulation of $\epsilon$ is allowed in theorems related to limits in real analysis?

Published on 13 Apr 2026 - 17:49

score 71 · Answer 13 · 2026-04-12 17:28:56

71

Views

A question about Cauchy sequence

Published on 12 Apr 2026 - 17:28

score 149 · Answer 14 · 2026-04-16 01:01:38

149

Views

Sequence of positive real numbers $(a_k)$ s.t. $\lim_{k \to \infty} a_k = 1$ and $\lim_{n \to \infty} a_1 a_2 \dots a_n = 0$

Published on 16 Apr 2026 - 1:01

score 61 · Answer 15 · 2026-04-11 08:42:56

61

Views

Is there any solution for the following recurrence problem

Published on 11 Apr 2026 - 8:42

List Question

What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?

Is there a formula for the sequence of numbers 3-6-9-12-15-18-21-24-27-30-36-42-48-54-60-66-72-78-84-90-102-114-126-138-150 etc..?

Convergence of iteration sequence

Divisibility property for sequence $a_{n+2}=-2(n-1)(n+3)a_n-(2n+3)a_{n+1}$

Find $\lim\limits_{n\to\infty}\sum\limits_{k=1}^n \frac{2k+1}{k^2(k+1)^2}$

Is the series $\sum_{n=1}^\infty (\sqrt[n]{a}-1)$ convergent or divergent?

Prove convergence of alternating sequence with factorial in denominator $\frac{\left(-5\right)^n}{n!}$

If $a,b,c$ are in $A.P.$ then prove that $b^2>ac$

Renyi's proof of Faddeev's theorem: convergence of a series

Sum $\sum(2n+1) × 2^n$

A problem from Makarov Selected Problems in Real Analysis

Why manipulation of $\epsilon$ is allowed in theorems related to limits in real analysis?

A question about Cauchy sequence

Sequence of positive real numbers $(a_k)$ s.t. $\lim_{k \to \infty} a_k = 1$ and $\lim_{n \to \infty} a_1 a_2 \dots a_n = 0$

Is there any solution for the following recurrence problem

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