Recent questions tagged convergence-divergence / GATE Overflow for GATE CSE

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1

ISI2015-MMA-24
The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to $-1$ $1$ $0$ does not converge

The series $\sum_{k=2}^{\infty} \frac{1}{k(k-1)}$ converges to$-1$$1$$0$does not converge

Arjun

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Arjun asked Sep 23, 2019

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2

ISI2015-MMA-56
Let $\{a_n\}$ be a sequence of non-negative real numbers such that the series $\Sigma_{n=1}^{\infty} a_n$ is convergent. If $p$ is a real number such that the series $\Sigma \frac{\sqrt{a_n}}{n^p}$ diverges, then $p$ must be strictly less than $\frac{1}{2}$ ... but can be greater than$\frac{1}{2}$ $p$ must be strictly less than $1$ but can be greater than or equal to $\frac{1}{2}$

Let $\{a_n\}$ be a sequence of non-negative real numbers such that the series $\Sigma_{n=1}^{\infty} a_n$ is convergent. If $p$ is a real number such that the series $\Si...

Arjun

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Arjun asked Sep 23, 2019

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3

ISI2016-MMA-22
The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if $a \in [-1, 1)$ $a \in (-1, 1]$ $a \in [-1, 1]$ $a \in (-\infty, \infty)$

The infinite series $\Sigma_{n=1}^{\infty} \frac{a^n \log n}{n^2}$ converges if and only if$a \in [-1, 1)$$a \in (-1, 1]$$a \in [-1, 1]$$a \in (-\infty, \infty)$

go_editor

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go_editor asked Sep 13, 2018

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