Two infinite geometric series are given as follows: Series I: Series II: If both…

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

Problem

Two infinite geometric series are given as follows: Series I:

8+8r+8r^{2}+8r^{3}+\dots

Series II:

5+5r^{2}+5r^{4}+5r^{6}+\dots

If both series converge and their sums are equal, then the value of

r

is (a)

-\dfrac{3}{5}

(b)

-\dfrac{3}{8}

(c)

\dfrac{3}{8}

(d)

\dfrac{3}{5}