Answer
$=\dfrac {1}{4}$
Work Step by Step
$\dfrac {1}{16}+\dfrac {3}{64}+\dfrac {9}{256}+\dfrac {27}{1024}=\dfrac {1}{16}+\dfrac {1}{16}\times \left( \dfrac {3}{4}\right) +\dfrac {1}{16}\times \left( \dfrac {3}{4}\right) ^{2}+\dfrac {1}{16}\times \left( \dfrac {3}{4}\right) ^{3}\ldots =\dfrac {a_{1}}{1-r};a_{1}=\dfrac {1}{16};r=\dfrac {3}{4}\Rightarrow S_{\infty }=\dfrac {\dfrac {1}{16}}{1-\dfrac {3}{4}}=\dfrac {1}{4}$
