Answer
$\frac{7}{2}$
Work Step by Step
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. It equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $|\frac{3}{7}|\lt1$.
Hence the sum: $\dfrac{2}{1-\frac{3}{7}}=\frac{7}{2}$