# if $\sum_{n=1}^{\infty}|a_n -a_{n-1}|<\infty$ then the series $\sum_{n=1}^{\infty}a_nx^n$,for all $x\in\mathbb{R}$, is convergent

by Arindam basak   Last Updated June 13, 2019 12:20 PM

if $$\sum_{n=1}^{\infty}|a_n -a_{n-1}|<\infty$$ then the series $$\sum_{n=1}^{\infty}a_nx^n$$,for all $$x\in\mathbb{R}$$, is convergent

1. nowhere on $$\mathbb{R}$$
2. everywhere on $$\mathbb{R}$$
3. on some set containing (-1,1)
4. only on (-1,1)
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