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

Geometry, a figure is made of a rectangle and an isosceles right triangle. ...

a figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r

Evalute right-hand limit, Evaluate following limits. Solution ...

Evaluate following limits. Solution Let's begin with the right-hand limit.  For this limit we have, x > 4  ⇒          4 - x 3   = 0      also, 4 - x → 0  as x → 4

GEOMETRIC PROGRESSION, THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPE...

THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPECTIVELY AND THE COMMON RATIO IS POSITIVE.FIND THE COMMON RATIO

How many hours will it take before the cars are 610 miles, Two commuters le...

Two commuters leave the similar city at the same time but travel in opposite directions. One car is traveling at an average speed of 63 miles per hour, and the other car is traveli

Calculus, what is the derivatives of y=u/5+7 and u=5x-35 using the chain ru...

what is the derivatives of y=u/5+7 and u=5x-35 using the chain rule?

Domain of a vector function - three dimensional space, Domain of a Vector F...

Domain of a Vector Function There is a Vector function of a single variable in R 2 and R 3 have the form, r → (t) = {f (t), g(t)} r → (t) = {f (t) , g(t), h(t)} co

Find the value of a+b, If A, B are acute angles and sinA= cosB, then find t...

If A, B are acute angles and sinA= cosB, then find the value of A+B. Ans:    A + B = 90 o

Application of linear equations, Application of Linear Equations We ar...

Application of Linear Equations We are going to talk about applications to linear equations.  Or, put in other terms, now we will start looking at story problems or word probl

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