Assuming that you have a series of a product $\sum_{l=0}^{\infty} f(l) g(l)$ and you know what $\sum_{l=0}^{\infty} f(l) $ is. Does this help, finding an approximate form for the whole series?
2026-04-11 23:54:35.1775951675
Series of product
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No, let $f(l)=1/(l^2)$, then your summation doesn't converge for $g(l)=l$, but it does for $g(l)=1$.