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JEE Math Practice Question

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

  1. A.$$\sqrt{2}$$
  2. B.1
  3. C.$$\frac{1}{\sqrt{2}}$$
  4. D.0

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