Answer
The sum is $10$. See the graph below:
Work Step by Step
From the graph, we can observe that the horizontal asymptote of the function is $y=10$.
Consider the series,
$4+4\times 0.6+4{{\left( 0.6 \right)}^{2}}+4{{\left( 0.6 \right)}^{3}}+\cdots $
The first term of the series is ${{a}_{1}}=4$ and common ratio is $r=0.6$.
The sum of an infinite geometric series with the first term ${{a}_{1}}$ and common ratio r is given by:
$S=\frac{{{a}_{1}}}{1-r}$
Substituting ${{a}_{1}}=4$ and $r=0.6$, we get,
$\begin{align}
& S=\frac{4}{1-0.6} \\
& =\frac{4}{0.4} \\
& =10
\end{align}$
So, the sum of the infinite series is 10.
