Question Number 50359 by prof Abdo imad last updated on 16/Dec/18
$$\left.\mathrm{1}\right)\:{calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{k}} \:{C}_{{n}} ^{{k}} \:\:\frac{\mathrm{1}}{{k}+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{S}_{{n}} \left({p}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \left(−\mathrm{1}\right)^{{k}} \:\:\:\frac{{C}_{{n}} ^{{k}} }{{p}+{k}+\mathrm{1}} \\ $$$${p}\:{integr}\:{natural}. \\ $$