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AP® Calculus AB-BC

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Moderate

Sum to Infinity of $\cfrac { 1 }{ ( 2n ) ! }$

APCALC-IQSTUB

What is the sum to infinity of the following series?

$$\sum _{ n=0 }^{ n=\infty }{ \cfrac { 1 }{ ( 2n ) ! } } $$

A

$\cfrac{ { e }^{ 2 }+1 }{2e}$

B

$\cfrac{ { e }^{ 2 }-1 }{e}$

C

$\cfrac{e+1 }{2e}$

D

$\cfrac{ { e }^{ 2 }+1 }{e}$