Approximate the Sum of the Series by Using the First $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 3 } { \ln ( n + 1 ) }$

Multiple Choice

Approximate the sum of the series by using the first six terms. $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 3 } { \ln ( n + 1 ) }$

A) $0.587 < S < 3.473$
B) $1.549 < S < 2.511$
C) $1.309 < S < 2.751$
D) $0.427 < S < 3.633$
E) $0.227 < S < 3.833$