lim_(x→∞) (1/( (√(n ))))( /( (√(n+1))))+( /( (√n)))(( 1)/( (√(n+2))))( / )+( /( (√n)))( /( (√(n+3))))(1/ )( / )+..............+( /( (√n)))(1/( (√(n+n))))( / )=? what answer


Question and Answers Forum

All Questions Topic List
Limits Questions
Previous in All Question Next in All Question
Previous in Limits Next in Limits
Question Number 129385 by Adel last updated on 15/Jan/21

$\lim_{x \to \infty} \frac{1}{\sqrt{n}} \frac{}{\sqrt{n + 1}} + \frac{}{\sqrt{n}} \frac{1}{\sqrt{n + 2}} \frac{}{} + \frac{}{\sqrt{n}} \frac{}{\sqrt{n + 3}} \frac{1}{} \frac{}{} + . . . . . . . . . . . . . . + \frac{}{\sqrt{n}} \frac{1}{\sqrt{n + n}} \frac{}{} = ?$ $w h a t a n s w e r$
	Answered by Dwaipayan Shikari last updated on 15/Jan/21

	$\lim_{n \to \infty} \underset{k = 1}{\sum^{n}} \frac{1}{\sqrt{n^{2} + n k}} = \frac{1}{n} \underset{k = 1}{\sum^{n}} \frac{1}{\sqrt{1 + \frac{k}{n}}} = \int_{0}^{1} \frac{1}{\sqrt{1 + x}} d x$ $= {[2 \sqrt{1 + x}]}_{0}^{1} = 2 \sqrt{2} - 2$
	Commented by Adel last updated on 15/Jan/21

	Thank you, madam, what is the name of the method you have used and you have taken this antigral from zero to one?
	Commented by Adel last updated on 16/Jan/21

	$answer sir$
	Commented by Adel last updated on 16/Jan/21

	$name of the method ?$
	Commented by Adel last updated on 18/Jan/21

	$name the method plese sir$
	Commented by Dwaipayan Shikari last updated on 22/Jan/21

	$R i e m a n n s u m s$ $Y o u c a n G o o g l e i t$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum