Answer
Converges to $0$
Work Step by Step
We can divide the sequence into two sub-sequences, namely, the odd-numbered terms ($\frac{1}{n}$) as $\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},...$ and the even-numbered terms ($\frac{1}{n+2}$) as $\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},...$ the other sub-sequence.
We can see that the limit of both sub-sequences is $0$ as $n \to \infty $ ; therefore, the limit of the sequence is $0$ as well.
Hence, the given sequence converges to $0$.
