JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

The sum of

n

terms of the series

1+(1+x)+\left(1+x+x^2\right)+\left(1+x+x^2+x^3\right)+\ldots

. where

x \neq 1

View answer and explanation

Correct option: C

\frac{n}{1-x}-\frac{x\left(1-x^n\right)}{(1-x)^2}

Option C (

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

) is correct because it is derived by summing the geometric series within each term and then summing the resulting series.

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