JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

\lim\limits_{x \to - 1} \frac{{\left( {1 + x} \right)\left( {1 - {x^2}} \right)\left( {1 + {x^3}} \right)\left( {1 - {x^4}} \right) \ldots \left( {1 - {x^{4n}}} \right)}}{{{{\left[ {\left( {1 + x} \right)\left( {1 - {x^2}} \right)\left( {1 + {x^3}} \right)\left( {1 - {x^4}} \right) \ldots \left( {1 - {x^{2n}}} \right)} \right]}^2}}}

is equal to

View answer and explanation

Correct option: A

^{4n}{C_{2n}}

Option A (

^{4n}{C_{2n}}

) is correct because after simplifying the expression and applying L'Hopital's rule repeatedly, the limit evaluates to the binomial coefficient

^{4n}{C_{2n}}

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