4 votes 4 votes What is the value of $1 + \dfrac{1}{4} + \dfrac{1}{16} + \dfrac{1}{64} + \dfrac{1}{256} + ......?$ $2$ $\dfrac{7}{4}$ $\dfrac{3}{2}$ $\dfrac{4}{3}$ Quantitative Aptitude gate2018-ec general-aptitude quantitative-aptitude number-series + – Lakshman Bhaiya asked Feb 21, 2018 • edited Jun 2, 2019 by Lakshman Bhaiya Lakshman Bhaiya 1.2k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 7 votes 7 votes 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 Ashwani Kumar 2 answered Feb 21, 2018 • edited Jun 21, 2019 by Lakshman Bhaiya Ashwani Kumar 2 comment Share Follow See all 0 reply Please log in or register to add a comment.