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)
Tags : power-series


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