Answer
Diverges
Work Step by Step
Consider the sequence \(\frac{n}{n+1}\). Rewrite it as \(\frac{n+1-1}{n+1}\). Taking the limit as \(n\) approaches infinity:
\[ \lim_{n\to\infty} \frac{n}{n+1} = \lim_{n\to\infty} \left(1 - \frac{1}{n+1}\right) = 1 \]
Since the limit is not equal to zero, the nth term test for divergence implies that the series \(\sum \frac{n}{n+1}\) diverges.
