The product 2^1/44^1/168^1/4816^1/128 to is equal to:

Question

The product $2^{1/4}\cdot4^{1/16}\cdot8^{1/48}\cdot16^{1/128}\cdots$ to $\infty$ is equal to:

Accepted Answer

$${2^{{1 \over 4}}}{.4^{{1 \over {16}}}}{.8^{{1 \over {48}}}}{.16^{{1 \over {128}}}}$$ ...

= $${2^{{1 \over 4} + {2 \over {16}} + {3 \over {48}} + ...\infty }}$$

= $${2^{{1 \over 4} + {1 \over 8} + {1 \over {16}} + ...\infty }}$$

= $${2^{\left( {{{{1 \over 4}} \over {1 - {1 \over 2}}}} \right)}}$$

= $${2^{{1 \over 2}}}$$

Solutions · 1