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Let, $a_{n} \;=\; \left ( 1-\frac{1}{\sqrt{2}} \right ) ... \left ( 1- \frac{1}{\sqrt{n+1}} \right )$ , $n \geq 1$. Then $\lim_{n\rightarrow \infty } a_{n}$

(A) equals $1$

(B) does not exist

(C) equals $\frac{1}{\sqrt{\pi }}$

(D) equals $0$

1 Answer

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Limit tends to zero.

Just take a calculator and verify for some range of values, you can observe that as we increase the value of n we will get a result close to zero.

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