GATE ECE 2018 | GA Question: 4

Question

What is the value of $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{256}+ \cdots?$

• A. $2$
• B. $\frac{7}{4}$
• C. $\frac{3}{2}$
• D. $\frac{4}{3}$

Answer 1

1 + $\dfrac{1}{4}$ + $\dfrac{1}{16}$ + $\dfrac{1}{64}$ + $\dfrac{1}{256}$ + ....

By seeing the above series we can identify the series as infinite G.P. series

Here 1st term i.e. a = 1 & common ratio i.e r = $\dfrac{1}{4}$

∴ The sum of the above infinite G.P series will be $\dfrac{1}{1 - \dfrac{1}{4} }$  = $\dfrac{4}{3}$  

∴ The answer is option D) $\dfrac{4}{3}$