The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots .$ to $\infty$ is equal to

  • [JEE MAIN 2020]
  • A

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

  • B

    $2^{\frac{1}{4}}$

  • C

    $2$

  • D

    $1$

Similar Questions

Let $a_1, a_2, a_3, \ldots$. be a $GP$ of increasing positive numbers. If the product of fourth and sixth terms is $9$ and the sum of fifth and seventh terms is $24 ,$ then $a_1 a_9+a_2 a_4 a_9+a_5+a_7$ is equal to $.........$.

  • [JEE MAIN 2023]

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How many terms of $G.P.$ $3,3^{2}, 3^{3}$... are needed to give the sum $120 ?$

In a geometric progression, if the ratio of the sum of first $5$ terms to the sum of their reciprocals is $49$, and the sum of the first and the third term is $35$ . Then the first term of this geometric progression is

  • [JEE MAIN 2014]

Find four numbers forming a geometric progression in which the third term is greater than the first term by $9,$ and the second term is greater than the $4^{\text {th }}$ by $18 .$