Consider the infinite geometric series 2k+2k ( k-1 k+1 )+2k ( k-1 k+1 )^2+

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

Problem

Consider the infinite geometric series

2k+2k\left(\dfrac{k-1}{k+1}\right)+2k\left(\dfrac{k-1}{k+1}\right)^2+\cdots.

If its sum to infinity equals

8

, then the value of

k

is (a)

k = 7

(b)

k = 2

(c)

k = \displaystyle \frac{-1+\sqrt{33}}{2}

(d)

k = \displaystyle \frac{1+\sqrt{33}}{2}