$\lim _{n\to \infty }\left{\left({2}^{\frac{1}{2}}-{2}^{\frac{1}{3}}\right)\left({2}^{\frac{1}{2}}-{2}^{\frac{1}{5}}\right)⋯⋯\left({2}^{\frac{1}{2}}-{2}^{\frac{1}{2n+1}}\right)\right}$ is equal to [JEE Main 2023, 6 Apr (Shift 2)]

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\(\lim _{n\to \infty }\left{\left({2}^{\frac{1}{2}}-{2}^{\frac{1}{3}}\right)\left({2}^{\frac{1}{2}}-{2}^{\frac{1}{5}}\ri…

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