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let-w-n-x-k-1-n-x-k-k-find-w-n-x-for-x-lt-1-2-find-lim-n-w-n-x-




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

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