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$2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \dots \infty is equal to$

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Correct option is B

S=14+28+316+…∞ →112S=18+216+332+…∞−⋯→21−2⇒S−12S=14+18+116+......=141−1/2=1/2 sum of infinite terms in G.P=a1-r12S=12→S=1given sum=2S=21=2.

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21/4⋅41/8⋅81/16…∞ is equal to

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$2^{1 / 4} \cdot 4^{1 / 8} \cdot 8^{1 / 16} \dots \infty is equal to$