It seems there might be some formatting issues, but I assume the series is:
$$\sum_{n=1}^{\infty} \left(2 + \frac{1}{n}\right)^{n}$$
Now, we will apply the root test. The root test states that if $\lim_{n\to\infty} \sqrt[n]{|a_n|} = L$, then:
Show more…