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Single Variable Calculus

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Moderate

Manipulating a Sum to Get a Geometric Series

SVCALC-GJV1F4

What is the sum of the series:

$$\sum_{n=0}^\infty \frac{5^{n+1}}{2^{3n}}$$

A

$\cfrac{2}{7}$

B

$\cfrac{5}{3}$

C

$\cfrac{8}{3}$

D

$\cfrac{40}{3}$

E

The series diverges