GATE2018 EC: GA-4

Question

What is the value of  $1 + \dfrac{1}{4} + \dfrac{1}{16} + \dfrac{1}{64} + \dfrac{1}{256} + ......?$

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

Answer 1

It is an infinite G.P. with first term $a=1$ and common ratio $r = \dfrac{1}{4}$.

Sum of infinite G.P with $|r| < 1$ is

$S_{\infty}=\dfrac{a}{1-r}$

$S_{\infty}=\dfrac{1}{1-\dfrac{1}{4}}$

$S_{\infty}=\dfrac{4}{3}$

Hence option d) is correct