JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Application +4 | -1

If sum of the series

\sum \limits_{n = 0}^\infty {r^n} = S

for

\left| r \right| < 1

, then sum of the series

\sum \limits_{n = 0}^\infty {r^{2n}}

, is

View answer and explanation

Correct option: D

\frac{{{S^2}}}{{2S - 1}}

Option D (

\frac{{{S^2}}}{{2S - 1}}

) is correct because by substituting the expression for r in terms of S, we find the sum of the series to be

\frac{{{S^2}}}{{2S - 1}}

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