Is there a closed-form of $\frac{1}{1}+\frac{1}{1+2^2}+\frac{1}{1+2^2+3^2}+.....$ How can I find the closed-form of?
$$\frac{1}{1}+\frac{1}{1+2^2}+\frac{1}{1+2^2+3^2}+.....$$
Any help thanks

Hint: The $n$-th term in the series is $\dfrac{1}{\sum_{k=1}^n k^2}=\dfrac{6}{n(n+1)(2n+1)}$. Use partial fractions.
