Question Number 165209 by HongKing last updated on 27/Jan/22
$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{k}}} {\sum}}\:\frac{\mathrm{n}^{\mathrm{2}} \:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{n}\pi}{\mathrm{2}}}{\mathrm{n}^{\mathrm{4}} \:\pi^{\mathrm{4}} \:+\:\mathrm{n}^{\mathrm{2}} \:\pi^{\mathrm{2}} \:\mathrm{a}\:+\:\mathrm{b}}\:=\:? \\ $$