find-the-value-of-s-1-p-1-q-1-1-p-2-q-2-and-s-2-p-1-q-1-pdivide-q-1-p-2-q-2-

Tinku Tara June 4, 2023 Limits 0 Comments

Question Number 30481 by abdo imad last updated on 22/Feb/18

find the value of s_1 = Σ_(p≥1,q≥1) (1/(p^2 q^2 )) and s_2 = Σ_(p≥1,q≥1 ,pdivide q) (1/(p^2 q^2 )) .

$${find}\:{the}\:{value}\:{of}\:\:{s}_{\mathrm{1}} =\:\sum_{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}} \:\:\frac{\mathrm{1}}{{p}^{\mathrm{2}} {q}^{\mathrm{2}} }\:\:\:{and} \\ $$$${s}_{\mathrm{2}} =\:\:\sum_{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}\:,{pdivide}\:{q}} \:\:\frac{\mathrm{1}}{{p}^{\mathrm{2}} {q}^{\mathrm{2}} }\:. \\ $$

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