Question

If $P_n=\prod _{k=0}^n{C}_k$, that is $P_n$ denote the product of all the binomial coefficients in ${(1+x)}^n$, then $\underset{n\to \infty }{lim}{P}_n{P}_{n+2}$ equals

• A. $e$
• B. $1$
• C. $\frac{1}{e}$
• D. None of these

Answer 1

The correct option is D None of these

As $n\to \infty$ , $P_n\to \infty$.

Therefore,

${lim}_{n\to \infty }{P}_n{P}_{n+2}=\infty$

Hence, the required limit does not exist.