JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

The sum of first 10 terms of the series

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

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Correct option: A

\left( {\frac{{{x^{20}} - 1}}{{{x^2} - 1}}} \right)\left( {\frac{{{x^{22}} + 1}}{{{x^{20}}}}} \right) + 20

Option A (

\left( {\frac{{{x^{20}} - 1}}{{{x^2} - 1}}} \right)\left( {\frac{{{x^{22}} + 1}}{{{x^{20}}}}} \right) + 20

) is correct because it represents the sum of the first 10 terms of the given series after simplification.

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