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AP® Calculus AB-BC

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Difficult

Converging Values Of $x$

APCALC-AWH28A

Find all values of $x$ for which:

$$\sum _{ n=0 }^{ \infty }{ n!{ \left( \cfrac { x }{ 5 } \right) }^{ n } } $$

...converges.

A

$ x = -1$ only

B

$x=0$ only

C

$ (-5, 5)$

D

$ [-5, 5]$