Question
$\lim _{x \rightarrow 1} \frac{(1-x)\left(1-x^{2}\right) \ldots\left(1-x^{2 n}\right)}{\left[(1-x)\left(1-x^{2}\right) \ldots\left(1-x^{n}\right)\right]^{2}}=$(A) $n !$(B) $\frac{(2 n) !}{n !}$(C) $\frac{(2 n) !}{(n !)^{2}}$(D) None of these
Step 1
Step 1: We are given the limit expression as $\lim _{x \rightarrow 1} \frac{(1-x)\left(1-x^{2}\right) \ldots\left(1-x^{2 n}\right)}{\left[(1-x)\left(1-x^{2}\right) \ldots\left(1-x^{n}\right)\right]^{2}}$. Show more…
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