Does the series ∑n=1∞n+1n+2\sum_{n=1}^{\infty} \frac{n+1}{n+2}∑n=1∞n+2n+1 converge?
No, because limn→∞an=1≠0\lim_{n \to \infty} a_n = 1 \neq 0limn→∞an=1=0
Yes, because it is a p-series
Yes, by the ratio test
No, because nnn is too large