What is the value of $1 + \dfrac{1}{4} + \dfrac{1}{16} + \dfrac{1}{64} + \dfrac{1}{256} + ......?$
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
64.3k questions
77.9k answers
244k comments
80.0k users