Question

Find all the positive integers k for which $7 \times 2^k+1$ is a perfect square

score 345 · Answer 1 · 2026-05-11 08:39:16

345

Views

Find all the positive integers k for which $7 \times 2^k+1$ is a perfect square

Published on 11 May 2026 - 8:39

score 885 · Answer 2 · 2026-05-10 13:49:16

885

Views

How to represent a sum of exponentials as one exponential

Published on 10 May 2026 - 13:49

score 93 · Answer 3 · 2026-04-15 15:37:00

93

Views

Series Expansion of $\frac{f(x)}{g(x)}$

Published on 15 Apr 2026 - 15:37

score 202 · Answer 4 · 2026-05-16 14:16:14

202

Views

Find the limit of $(1^7 + 2^7 + .......+ n^7)^{1/n}$ as $n \rightarrow \infty$

Published on 16 May 2026 - 14:16

score 33 · Answer 5 · 2026-04-12 14:16:24

33

Views

Analytical convergence of an equation?

Published on 12 Apr 2026 - 14:16

score 107 · Answer 6 · 2026-05-16 14:15:53

107

Views

Finding the limit of $2^{-1/\sqrt {n}}$ as $n \rightarrow \infty$.

Published on 16 May 2026 - 14:15

score 66 · Answer 7 · 2026-04-24 09:38:45

66

Views

Real analysis problems involving proofs with sequences and sets

Published on 24 Apr 2026 - 9:38

score 38 · Answer 8 · 2026-04-17 13:29:29

38

Views

A confusion in understanding the prove that the sequence ${(a_{n})^{1/n}}$ where $a_{n+m} \leq a_{n}a_{m}$ is convergent.

Published on 17 Apr 2026 - 13:29

score 66 · Answer 9 · 2026-04-15 00:26:44

66

Views

Show that for a.e. $x\in[0,1]$, $\sum_{n=1}^\infty\sum_{k=1}^n\dfrac{1}{n^\gamma}\dfrac{1}{\sqrt{|x-\frac{k}{2^n}|}}$ converges.

Published on 15 Apr 2026 - 0:26

score 70 · Answer 10 · 2026-04-16 20:22:42

70

Views

If $(a_n)_{n=1}^{\infty}$ is a converging sequence, and for all $n ∈ Z +, a_n ≤ 1$, then $lim_{n→∞} a_n ≤ 1$

Published on 16 Apr 2026 - 20:22

score 127 · Answer 11 · 2026-04-17 08:53:25

Calculating the sum of the infinite series $\frac{1}{5} + \frac{1}{3}\frac{1}{5^3} + \frac{1}{5} \frac{1}{5^5} +......$

score 114 · Answer 12 · 2026-04-14 16:40:19

114

Views

Does the series $\sum_{ n = 0}^{\infty } \frac{1}{\sqrt{n}}\ln\bigl(1+\frac{1}{\sqrt{n}}\bigr)$ converge?

Published on 14 Apr 2026 - 16:40

score 59 · Answer 13 · 2026-04-15 00:05:28

59

Views

Understanding Gaps in concept of Radius of Convergence of Power Series

Published on 15 Apr 2026 - 0:05

score 92 · Answer 14 · 2026-04-11 19:07:52

92

Views

does the series $\frac{\ln(n^{n})}{n!}$ converge?

Published on 11 Apr 2026 - 19:07

score 50 · Answer 15 · 2026-04-15 03:00:38

50

Views

Looking for formula or closed form for this series

Published on 15 Apr 2026 - 3:00

List Question

Find all the positive integers k for which $7 \times 2^k+1$ is a perfect square

How to represent a sum of exponentials as one exponential

Series Expansion of $\frac{f(x)}{g(x)}$

Find the limit of $(1^7 + 2^7 + .......+ n^7)^{1/n}$ as $n \rightarrow \infty$

Analytical convergence of an equation?

Finding the limit of $2^{-1/\sqrt {n}}$ as $n \rightarrow \infty$.

Real analysis problems involving proofs with sequences and sets

A confusion in understanding the prove that the sequence ${(a_{n})^{1/n}}$ where $a_{n+m} \leq a_{n}a_{m}$ is convergent.

Show that for a.e. $x\in[0,1]$, $\sum_{n=1}^\infty\sum_{k=1}^n\dfrac{1}{n^\gamma}\dfrac{1}{\sqrt{|x-\frac{k}{2^n}|}}$ converges.

If $(a_n)_{n=1}^{\infty}$ is a converging sequence, and for all $n ∈ Z +, a_n ≤ 1$, then $lim_{n→∞} a_n ≤ 1$

Calculating the sum of the infinite series $\frac{1}{5} + \frac{1}{3}\frac{1}{5^3} + \frac{1}{5} \frac{1}{5^5} +......$

Does the series $\sum_{ n = 0}^{\infty } \frac{1}{\sqrt{n}}\ln\bigl(1+\frac{1}{\sqrt{n}}\bigr)$ converge?

Understanding Gaps in concept of Radius of Convergence of Power Series

does the series $\frac{\ln(n^{n})}{n!}$ converge?

Looking for formula or closed form for this series

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