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

Algorithm for division, Also, their inability to apply the algorithm for di...

Also, their inability to apply the algorithm for division becomes quite evident. The reason for these difficulties may be many. We have listed some of them below. 1) There are n

Circumcircle problem, find the radius of circumcircle of an equilateral tri...

find the radius of circumcircle of an equilateral triangle of 6root3 one side.

Example of fractional equations, Example of Fractional Equations: Exa...

Example of Fractional Equations: Example: Solve the fractional equation (3x +8)/x +5 =0 Solution: Multiply both sides of the equation by the LCD (x). (x) ((3x

Hyperboloid of one sheet - three dimensional spaces, Hyperboloid of One She...

Hyperboloid of One Sheet The equation which is given here is the equation of a hyperboloid of one sheet. x 2 /a 2 + y 2 /b 2 - z 2 /c 2 = 1 Here is a diagram of a com

Generalized least squares regression, a. Estimate the following model,  C t...

a. Estimate the following model,  C t   =  β 0   +  β 1 * DI t +  ε t             Where C t = Aggregate Consumption Expenditure in Australia, quarterly data for the per

Construct the adjacency matrix and the adjacency lists, Question: Constrcut...

Question: Constrcut the adjacency matrix and the adjacency lists for the graph G below, where the weights associated with edges represent distances between nodes. If no edge is pre

Actaap released item booklet april 2010 grade 8, what is the least number o...

what is the least number of faces and bases the paperweight could have?

surfaces z + |y| = 1, Describe and sketch the surfaces z + |y| = 1 and (x ...

Describe and sketch the surfaces z + |y| = 1 and (x   2) 2 y + z 2 = 0.

Objective functions, For schedule consistency, you decide to require each o...

For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you

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