Convergence test for the following series The series is :-
$$ \frac{1}{1^2} + \frac{1+2}{1^2+2^2} + \frac{1+2+3}{1^2+2^2+3^2} + ... ∞ $$
I am unable to think for its general term.
Can anybody help me solve this.
Thanks in advance.

hint
$$1+2+3+....n=\frac{n}{2}(n+1)$$
$$1+2^2+3^2+...n^2=\frac{n}{6}(n+1)(2n+1)$$
for the another series, use the ratio test
$$\frac{a_{n+1}}{a_n}=\frac{(n+1)^2}{(n+1)!}\frac{n!}{n^2}=\frac{(n+1)^2}{(n+1)n^2}=\frac{n+1}{n^2}=\frac{1}{n}+\frac{1}{n^2}$$
the limit is zero when $n\rightarrow \infty$, so the series converges
