Question Number 30443 by abdo imad last updated on 22/Feb/18
$${let}\:\:{w}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{x}^{{k}} }{{k}}\:\:{find}\:{w}_{{n}} \left({x}\right)\:{for}\:\mid{x}\mid<\mathrm{1}\: \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} {w}_{{n}} \left({x}\right). \\ $$