Determine the Radius of Convergence for the Given Power Series $\sum _ { k = 0 } ^ { \infty } \frac { k x ^ { k } } { 4 ^ { k + 1 } }$

Multiple Choice

Determine the radius of convergence for the given power series. $\sum _ { k = 0 } ^ { \infty } \frac { k x ^ { k } } { 4 ^ { k + 1 } }$

A) $R =$ 4
B) $R =$ $\infty$
C) $R = \frac { 1 } { 4 }$
D) $R =$ 0