JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The sum of n terms of the series

1 + \left( {1 + x} \right) + \left( {1 + x + {x^2}} \right) + \;...

will be

View answer and explanation

Correct option: C

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

Option C,

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

, is correct because it represents the sum of the given series after simplification using the formula for the sum of a geometric progression.

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