lim {(2^{1/2}- 2^{1/3}) (2^{1/2} - 2^{1/5}) ..... (2^{1/2} - 2^{1/2n+1})} ; x ∈ (n → ∞) is equal to

Question

\(\lim\limits_{n \to \infty}\left\{(2^{1/2}-2^{1/3})(2^{1/2}-2^{1/5})...(2^{1/2}-2^{^{\frac{1}{2n+1}}})\right\}\) is equal to

(1) 1/√2 

(2) 1 

(3) √2 

(4) 0

Answer 1

Correct option is (4) 0