JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

\left| a \right| < 1

and

\left| b \right| < 1,

then the sum of the series

a\left( {a + b} \right) + {a^2}\left( {{a^2} + {b^2}} \right) + {a^3}\left( {{a^3} + {b^3}} \right) + \ldots

upto

\infty

, is

View answer and explanation

Correct option: B

\frac{{{a^2}}}{{1 - {a^2}}} + \frac{{ab}}{{1 - ab}}

Option B (

\frac{{{a^2}}}{{1 - {a^2}}} + \frac{{ab}}{{1 - ab}}

) is correct because the series can be split into two geometric series, and their sums can be calculated.

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