Answer
$infinite\ geometric\ series$, $1$, $\frac{a_1}{1-r}$, $|r|\geq 1$.
Work Step by Step
We can see that the series of the elements in the summation form is a geometric sequence. Thus, an infinite sum of the form $a_1+a_1r+a_1r^2+a_1r^3+$ is called an $infinite\ geometric\ series$. If $-1\lt r \lt 1$, its sum, $S$, is given by the formula $S=\frac{a_1}{1-r}$. The series does not have a sum if $|r|\geq 1$.
