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Moderate

Pointwise Limits and Uniform Convergence of a Series

TOPO-Y5NLC1

Which of the following statements are true?

Select ALL that apply.

A

$\sum\limits_{i=1}^{\infty} x^{n}$ converges uniformly on $(-1,1)$.

B

$\sum\limits_{i=1}^{\infty} x^{n}$ converges uniformly on any compact set in $(-1,1)$.

C

$\sum\limits_{i=1}^{\infty} x^{n}$ has a radius of convergence of $1$.

D

$\sum\limits_{i=1}^{\infty} x^{n}$ converges uniformly on $[-1,1]$.