Recall that for an infinite geometric series of the form
\(\displaystyle\sum_{n=0}^\infty ar^n\)
as long as \(|r|<1\), the series converges to the value \(\dfrac{a}{1-r}\).
Here you have \(r=-\dfrac23\), so the series converges. You have
\(\displaystyle\sum_{n=0}^\infty 5\left(-\dfrac23\right)^n=\dfrac5{1-\left(-\dfrac23\right)}=3\)
