The sum of the infinite series

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The sum of the infinite series,

1^2 - \frac{2^2}{5} + \frac{3^2}{5^2} - \frac{4^2}{5^3} + \frac{5^2}{5^4} - \frac{6^2}{5^5} + \dots

is : (a)

\frac{1}{2}

(b)

\frac{25}{24}

(c)

\frac{25}{54}

(d)

\frac{125}{252}