Did I solve this problem correctly? $\sum_{n=1}^{\infty}(-1)^{n+1}\frac{n^2}{n^3+4}$ For the following series:
$\sum_{n=1}^{\infty}(-1)^{n+1}\frac{n^2}{n^3+4}$
I found $b_n$ to be $b_n=\frac{n^2}{n^3+4} \gt 0$ and then I took the limit of this and found it to be zero.

You can prove that $b_n$ is decreasing by using the first derivative test (for the function to be decreasing $f'(x)<0$) and considering the function
$$ f(x)=\frac{x^2}{x^3+4}, \quad x\geq 2 . $$
