let give u_(n,k) = (1/(n+1)) +(1/(n+2)) +.... (1/(kn)) k integr fixed ≥2 find lim_(n→+ ∞) u


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Question Number 28891 by abdo imad last updated on 31/Jan/18

$l e t g i v e u_{n, k} = \frac{1}{n + 1} + \frac{1}{n + 2} + . . . . \frac{1}{k n} k i n t e g r f i x e d ⩾ 2$ $f i n d {l i m}_{n \to + \infty} u_{n, k} .$
	Answered by ajfour last updated on 01/Feb/18

	$u = \underset{r = 1}{\sum^{n (k - 1)}} \frac{1 / n}{1 + \frac{r}{n}} = \int_{0}^{k - 1} \frac{d x}{1 + x}$ $= \ln (1 + x) ∣_{0}^{k - 1} = \ln k .$
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