Answer
$20$
Work Step by Step
We will consider the theorem of convergence of an Infinite Geometric Series in order to solve this probelm.
The infinite geometric series $\displaystyle \sum_{k=1}^{\infty}a_{1}r^{k-1}$ converges when $|r| \lt 1,$and then its sum can be calculated as:
$\displaystyle \sum_{k=1}^{\infty}a_{1}r^{k-1}=\frac{a_{1}}{1-r}=S_\infty$
where r is the common ratio.
Since $r=0.95 \lt 1$, this shows that the infinite geometric series converges.
Its sum will be : $S_\infty=\dfrac{a_{1}}{1-r}=\displaystyle \frac{1}{1-0.95}=20$
