Question

Given $a>0 $, let $\sum_{n=1}^{\infty}a^{n^{2}}(x-1)^{n}$ check for which values of $x$ as $x\in\mathbb{R}$, the power series converges.

score 109 · Answer 1 · 2026-04-13 17:40:14

109

Views

Given $a>0 $, let $\sum_{n=1}^{\infty}a^{n^{2}}(x-1)^{n}$ check for which values of $x$ as $x\in\mathbb{R}$, the power series converges.

Published on 13 Apr 2026 - 17:40

score 109 · Answer 2 · 2026-04-13 04:25:45

109

Views

Kolakoski sequence collapse

Published on 13 Apr 2026 - 4:25

score 33 · Answer 3 · 2026-04-11 08:21:11

33

Views

Proof verification.Limit of sequence by definition.

Published on 11 Apr 2026 - 8:21

score 101 · Answer 4 · 2026-04-13 18:42:52

101

Views

How can I show that :$\sum_{n=1}^{\infty}(-1)^{n-1}(\zeta(n+1)-1))=\frac12$?

Published on 13 Apr 2026 - 18:42

score 1.8k · Answer 5 · 2026-04-16 16:23:43

1.8k

Views

Sequences Eventually and Frequently in a Set

Published on 16 Apr 2026 - 16:23

score 457 · Answer 6 · 2026-05-10 13:50:39

457

Views

Is this class of series all demonstrably transcendental?

Published on 10 May 2026 - 13:50

score 169 · Answer 7 · 2026-04-25 04:07:30

169

Views

Building neighborhoods around arbitrary real numbers that will contain "minimal" number of elements from the sequence $a_n=n\sin \frac{\pi n}{4}$

Published on 25 Apr 2026 - 4:07

score 180 · Answer 8 · 2026-05-14 07:25:55

180

Views

Curve Fitting for a sequence

Published on 14 May 2026 - 7:25

score 559 · Answer 9 · 2026-04-15 17:36:32

559

Views

$x_n \to x \in \mathbb{R}$ and $y_n \to 0 $. What about $\frac{x_n}{y_n}$?

Published on 15 Apr 2026 - 17:36

score 122 · Answer 10 · 2026-04-16 07:48:26

122

Views

Is this series conditionally convergent or absolutely convergent? $ \sum_{k=1}^{\infty}\left(-1\right)^{k+1}\frac{k^{k}}{\left(k+1\right)^{k+1}} $

Published on 16 Apr 2026 - 7:48

score 78 · Answer 11 · 2026-05-10 21:12:36

78

Views

Is this series conditionally convergent or absolutely convergent? $\sum_{k=1}^{\infty}\left(-1\right)^{k+1}\sin\left(\frac{1}{k}\right)$

Published on 10 May 2026 - 21:12

score 543 · Answer 12 · 2026-04-25 11:46:06

543

Views

Does the sequence $2n^2 +2n + 1$ consist only of primes and semiprimes?

Published on 25 Apr 2026 - 11:46

score 16.7k · Answer 13 · 2026-05-10 15:09:54

16.7k

Views

How to find the sum of a geometric series with a negative common ratio?

Published on 10 May 2026 - 15:09

score 137 · Answer 14 · 2026-04-15 03:06:15

137

Views

If $(x_n) \rightarrow 2$ then $(\frac{2x_n -1}{3}) \rightarrow 1$

Published on 15 Apr 2026 - 3:06

score 67 · Answer 15 · 2026-04-16 21:30:05

67

Views

which one is the correct option ? 1){$a_n$} is bounded and {$b_n$} is Bounded 2) atleast one of {$a_n$}, {$b_n$} is bounded

Published on 16 Apr 2026 - 21:30

List Question

Given $a>0 $, let $\sum_{n=1}^{\infty}a^{n^{2}}(x-1)^{n}$ check for which values of $x$ as $x\in\mathbb{R}$, the power series converges.

Kolakoski sequence collapse

Proof verification.Limit of sequence by definition.

How can I show that :$\sum_{n=1}^{\infty}(-1)^{n-1}(\zeta(n+1)-1))=\frac12$?

Sequences Eventually and Frequently in a Set

Is this class of series all demonstrably transcendental?

Building neighborhoods around arbitrary real numbers that will contain "minimal" number of elements from the sequence $a_n=n\sin \frac{\pi n}{4}$

Curve Fitting for a sequence

$x_n \to x \in \mathbb{R}$ and $y_n \to 0 $. What about $\frac{x_n}{y_n}$?

Is this series conditionally convergent or absolutely convergent? $ \sum_{k=1}^{\infty}\left(-1\right)^{k+1}\frac{k^{k}}{\left(k+1\right)^{k+1}} $

Is this series conditionally convergent or absolutely convergent? $\sum_{k=1}^{\infty}\left(-1\right)^{k+1}\sin\left(\frac{1}{k}\right)$

Does the sequence $2n^2 +2n + 1$ consist only of primes and semiprimes?

How to find the sum of a geometric series with a negative common ratio?

If $(x_n) \rightarrow 2$ then $(\frac{2x_n -1}{3}) \rightarrow 1$

which one is the correct option ? 1){$a_n$} is bounded and {$b_n$} is Bounded 2) atleast one of {$a_n$}, {$b_n$} is bounded

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