Let $X,Y$ be two random variables with joint probability mass function $$p_{X,Y}(k,l)=\begin{cases} \frac{6}{\pi^2(k+l-1)^3},\, k,l\in\mathbb{N},\\ 0, \text{ otherwise}. \end{cases}$$ Now I need to calculate the pmf of $Z=X+Y-1$. We have $$p_Z=\frac{6}{\pi^2}\sum_{k\in\mathbb{N}}\sum_{l\in\mathbb{N}} \mathbb{1}_{\{k+l-1=m\}}\cdot\frac{1}{(k+l-1)^3}$$ But I don't know how I can calculate this sum. Any help is greatly appreciated.
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