Answer
Convergent
16
Work Step by Step
$4+3+\dfrac {9}{4}+\dfrac {27}{16}\ldots =\sum ^{\infty }_{k=0}4\times \left( \dfrac {3}{4}\right) ^{k}\Rightarrow \lim _{k\rightarrow \infty }4\times \left( \dfrac {3}{4}\right) ^{k}=0$
$\sum ^{\infty }_{0}4\times \left( \dfrac {3}{4}\right) ^{k}-\dfrac {a_{1}}{1-r};a_{1}=4;r=\dfrac {3}{4}\Rightarrow S_{\infty }=\dfrac {4}{1-\dfrac {3}{4}}=16$
