Differential calculus, Mathematics

Assignment Help:

lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x?

Ans) all no.s are positive or 0. so limit is either positive or 0.........(1)

now {x}<=1;{2x}<=1;......

{x}+{2x}+....{nx}<=n

that implies lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity n/n^2;

that means lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity 1/n i.e. 0........(2)

from (1) and (2);

required limit=0;


Related Discussions:- Differential calculus

How tall was peter when he turned 15, Peter was 60 inches tall on his thirt...

Peter was 60 inches tall on his thirteenth birthday. By the time he turned 15, his height had increased 15%. How tall was Peter when he turned 15? Find 15% of 60 inches and add

Earth Day Bags, #question.I headed into Target in Webster, NY for an advert...

#question.I headed into Target in Webster, NY for an advertized free Earth Day Bag in (local newspaper and on your entrance store doors) and at 10:30 a.m. on Sunday, April 22nd, th

Square and square root., the value of square root of 200multiplied by squar...

the value of square root of 200multiplied by square root of 5+

Simplifying rational expressions, I need to simple this rational expression...

I need to simple this rational expression, but I can''t figure out how. (x+1)/(x^2-2x-35)+(x^2+x-12)/(x^2-2x-24)(x^2-4x-12)/(x^2+2x-15)

Geometry, prove angle MJL is congruent to angle KNL

prove angle MJL is congruent to angle KNL

Find x if circle passes through -3, The centre of a circle is (2x - 1, 3x +...

The centre of a circle is (2x - 1, 3x + 1).Find x if the circle passes through (-3,-1) and the length of the diameter is 20 units.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd