Question

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

• A. $1$
• B. $2$
• C. $3/2$
• D. $5/2$

Answer 1

The correct option is B $2$

$2^{\frac{1}{4}}{2}^{\frac{2}{8}}{2}^{\frac{3}{16}}{2}^{\frac{4}{32}}.......\infty$

$=2^{\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+\frac{4}{32}+}.....$

$=2^5$

where $S=\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+\frac{4}{32}+.$...

$\frac{S}{2}=\frac{1}{8}+\frac{2}{16}+\frac{3}{32}+$....

$\frac{S}{2}=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+$ ...

$\frac{\frac{1}{4}}{1-\frac{1}{2}}=\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{4}\times 2=\frac{1}{2}$

$\frac{S}{2}=\frac{1}{2}$

$\Rightarrow S=1.$

$\therefore G.E=2^{\prime }=2.$