$\text { Consider the series } \sum _ { n = 1 } ^ { \infty } \frac { 1 } { ( 6 n - 1 ) ^ { 2 } } \text {. The sum of the series is } \pi ^ { 2 } / 6 \text { Find the sum of }$ the series $\sum _ { n = 5 } ^ { \infty } \frac { 1 } { ( 6 n - 1 ) ^ { 2 } }$.
A) $1.5932$
B) $1.5632$
C) $1.6132$
D) $1.6232$
E) $1.5732$

Question

Quizplus · Accepted Answer

The sum of the series from $ n = 1 $ to $ \infty $ is $\pi^2/6$. To find the sum from $ n = 5 $ to $ \infty $, subtract the sum of the first four terms from $\pi^2/6$. Calculating these terms and subtracting gives approximately 1.5932.

The Series ∑n=5∞1(6n−1)2\sum _ { n = 5 } ^ { \infty } \frac { 1 } { ( 6 n - 1 ) ^ { 2 } }∑n=5∞​(6n−1)21​

The Series $\sum _ { n = 5 } ^ { \infty } \frac { 1 } { ( 6 n - 1 ) ^ { 2 } }$