JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

Sum of the series

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

terms is

View answer and explanation

Correct option: A

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

Option C (

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

) is correct because the sum of the series can be found by expressing each term as a geometric series and then summing the resulting series.

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