Given the Series $\sum _ { m - 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$

Multiple Choice

Given the series $\sum _ { m - 1 } ^ { \infty } \frac { 3 m } { 4 ^ { m } ( 3 m + 5 ) }$ estimate the error in using the partial sum $s _ { 8 }$ by comparison with the series $\sum _ { m - 9 } ^ { \infty } \frac { 1 } { 4 ^ { m } }$ .

A) $R _ { 8 } \leq 2.6130051$
B) $R _ { 8 } \geq 0.0000052$
C) $R _ { 8 } \leq 0.0000051$
D) $R _ { 8 } \geq 0.0000051$
E) $R _ { 8 } \leq 0.000005$