JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

The product

2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \ldots

\infty

is equal to:

View answer and explanation

Correct option: A

2^{\frac{1}{2}}

Option A (

2^{\frac{1}{2}}

) is correct because by expressing each term as a power of 2 and summing the exponents, we obtain a G.P. with a sum of 1/2, resulting in

2^{\frac{1}{2}}

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