Find lim_(n→∞) ((1/n^2 )+(2/n^2 )+(3/n^2 )+...(n/n^2 ))


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Question Number 192453 by Spillover last updated on 18/May/23

$F i n d \lim_{n \to \infty} (\frac{1}{n^{2}} + \frac{2}{n^{2}} + \frac{3}{n^{2}} + . . . \frac{n}{n^{2}})$
	Answered by senestro last updated on 18/May/23

	$1 / 2$
	Answered by deleteduser1 last updated on 18/May/23

	$\frac{1}{n^{2}} (\frac{n (n + 1)}{2}) = \frac{n + 1}{2 n} = \frac{1}{2} + \frac{1}{2 n} \Rightarrow \underset{n \to \infty}{l i m} (\underset{p = 1}{\sum^{n}} \frac{p}{n^{2}}) = \frac{1}{2}$
	Commented by Spillover last updated on 19/May/23

	$g r e a t .$
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