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k-1-m-1-n-n-m-1-nk-m-1-nk-m-




Question Number 148441 by qaz last updated on 28/Jul/21
Σ_(k=1) ^∞ Σ_(m=1) ^n ((n(m−1))/((nk+m−1)(nk+m)))=?
$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{m}−\mathrm{1}\right)}{\left(\mathrm{nk}+\mathrm{m}−\mathrm{1}\right)\left(\mathrm{nk}+\mathrm{m}\right)}=? \\ $$

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