Question

1 + $\frac{3}{2}$ + $\frac{5}{2^2}$ + $\frac{7}{2^3}$ + ......... ∞ is equal to

• A. 3
• B. 6
• C. 9
• D. 12

Answer 1

The correct option is D

12

It is an arithmetic-geometric series

$S_{\infty }$ = $\frac{a}{1-r}$ + $\frac{dr}{(1-r{)}^2}$ = $\frac{1}{1-\frac{1}{2}}$ + $\frac{2}{(1-\frac{1}{2}{)}^2}$ = $\frac{2}{\frac{1}{2}}$ + $\frac{2}{\frac{1}{4}}$

= 4 + 8 = 12.