Answer
$10$
Work Step by Step
THEOREM: Convergence of an Infinite Geometric Series
If $|r| \lt 1,$ the infinite geometric series $\displaystyle \sum_{k=1}^{\infty}a_{1}r^{k-1}$ converges. Its sum is
$\displaystyle \sum_{k=1}^{\infty}a_{1}r^{k-1}=\frac{a_{1}}{1-r}$
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Since $r=0.90$, the infinite geometric series converges.
$S=\displaystyle \frac{1}{1-0.90}=10$
