Question Number 50380 by prof Abdo imad last updated on 16/Dec/18
$$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}−{a}\right)^{{n}} \left({x}−{b}\right)^{{n}} } \\ $$$${witha}\neq{b} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{{C}_{{p}+{k}−\mathrm{1}} ^{{k}} }{\mathrm{2}^{{k}+{p}} }\: \\ $$$$+\:\sum_{{k}=\mathrm{0}} ^{{p}−\mathrm{1}} \:\:\:\frac{{C}_{{n}+{k}−\mathrm{1}} ^{{k}} }{\mathrm{2}^{{k}+{n}} } \\ $$