JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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The expression

{\left( {1 + \frac{{{x^2}}}{{2!}} + \frac{{{x^4}}}{{4!}} + \frac{{{x^6}}}{{6!}} + ...\infty } \right)^2}

will be represented in ascending power of

x

View answer and explanation

Correct option: D

1 + \frac{{{{\left( {2x} \right)}^2}}}{{2.2!}} + \frac{{{{\left( {2x} \right)}^4}}}{{2.4!}} + ...\infty

Option D (

1 + \frac{{{{\left( {2x} \right)}^2}}}{{2.2!}} + \frac{{{{\left( {2x} \right)}^4}}}{{2.4!}} + ...\infty

) is correct because it represents the given expression in ascending powers of x after simplification using exponential series.

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