Let , then equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

Let

S_k = \sum_{i=0}^{\infty} \frac{1}{(k+1)^i}

, then

\sum_{k=1}^{n} kS_k

equal : (a)

\frac{n(n+1)}{2}

(b)

\frac{n(n-1)}{2}

(c)

\frac{n(n+2)}{2}

(d)

\frac{n(n+3)}{2}