Question

$2^{1/4}\cdot 2^{2/8}\cdot 2^{3/16}\cdot 2^{4/32}\dots \infty$ is equal to -

• A. 1
• B. 2
• C. 3 / 2
• D. 5 / 2

Answer 1

Answer: (B)

The given product $=2^{\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+\frac{4}{32}+\dots .}=2^s$ (say)
Now $S=\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+\frac{4}{32}+.....\dots (1)$
$\Rightarrow \frac{1}{2}S=\frac{1}{8}+\frac{2}{16}+\frac{3}{32}+\dots \dots (2)$
$\therefore (1)-(2)$
$\Rightarrow \frac{1}{2}S=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\dots$
$=\frac{1/4}{1-1/2}=\frac{1}{2}$
$\therefore S=1$
$\Rightarrow$ Product $=2^1=2$