Question

Find the sum upto infinite terms.
$\frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\frac{4}{16}+....$

• A. $1$
• B. $4$
• C. $2$
• D. None of these

Answer 1

Answer: (C)

$2$

Given series:

$S=\frac{1}{2}+\frac{2}{4}+\frac{3}{8}+\frac{4}{16}+......$ .....(1)

Multiplying by $\frac{1}{2}$ on both sides

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

eq(1) - eq(2)

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

$\therefore S=2$

Hence, the answer is $2$.