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let-S-n-x-k-1-n-x-k-k-find-a-equivalent-of-S-n-x-when-n-




Question Number 42020 by math khazana by abdo last updated on 16/Aug/18
let  S_n (x)=Σ_(k=1) ^n  (x^k /( (√k)))  find a equivalent of S_n (x) when n→+∞
$${let}\:\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{x}^{{k}} }{\:\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \left({x}\right)\:{when}\:{n}\rightarrow+\infty \\ $$

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