Find the Sum of the Convergent Series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 1 } { 4 ^ { 2 n + 1 } ( 2 n + 1 ) }$

Multiple Choice

Find the sum of the convergent series $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { 1 } { 4 ^ { 2 n + 1 } ( 2 n + 1 ) }$ by using a well-known function. Round your answer to four decimal places.

A) 0.1419
B) 0.2450
C) 0.8961
D) 0.1651
E) 0.1974