Answer
Diverges
Work Step by Step
The given series can be made into a similar form as the definition of the geometric series.
We can reach the textbook form by inputting $n=1$ to get the initial term $a$ and see the factor difference when inputting $n=2$.
Note that the summation of an infinite geometric series is $S= \frac{a}{1-r}$ if |$r$| $\lt 1 $ , here $r$ is the common ratio of the geometric series.
Now, If we choose n = 1 we can see that the initial term is $a$ = $e^{2}$ and the common ratio $r$ = $\frac{e^{2}}{6}$ (Just by dividing any latter term by its former).
|$r$| = $\frac{e^{2}}{6}\approx 1.232 \gt 1 $
Thus, this geometric series diverges.
