If be roots of the equation and

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

\alpha, \beta

be roots of the equation

375x^2 - 25x - 2 = 0

and

s_n = \alpha^n + \beta^n

, then

\lim_{n \to \infty} \left( \sum_{r=1}^{n} s_r \right) = \dots

(a)

\frac{1}{12}

(b)

\frac{1}{4}

(c)

\frac{1}{3}

(d) 1