Sequences And Series

Sum of first ' $n$ ' terms of a series $a_1+a_2+\ldots+a_n$ is given by $S_n=\frac{n\left(n^2-1\right)(n+2)}{4}$, then the value of $\lim _\limits{n \rightarrow \infty} \sum_\limits{r=2}^n \frac{1}{a_r}$ is