Answer
$1\times \dfrac {\left( \left( \dfrac {1}{4}\right) ^{11}-1\right) }{\dfrac {1}{4}-1}=\dfrac {1398101}{1048576}$
Work Step by Step
$\sum ^{10}_{k=0}\left( \dfrac {1}{4}\right) ^{k}=\dfrac {a_{1}\left( r^{n}-1\right) }{r-1};a_{1}=\left( \dfrac {1}{4}\right) ^{0}=1;r=\dfrac {1}{4};n=11\Rightarrow S_{n}=1\times \dfrac {\left( \left( \dfrac {1}{4}\right) ^{11}-1\right) }{\dfrac {1}{4}-1}=\dfrac {1398101}{1048576}$
