AP® Calculus AB-BC

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Difficult

An Infinite Geometric Sum

APCALC-1J5ETI

Find the indicated sum:

$$\sum _{ k=n }^{ \infty }{ { \left( \cfrac { 3 }{ 4 } \right) }^{ k } } $$

A

$3-{ \left( \cfrac { 3 }{ 4 } \right) }^{ n }$

B

$3$

C

$4\cdot { \left( \cfrac { 3 }{ 4 } \right) }^{ n }$

D

$\cfrac{3^{n}}{4^{n-1}}$