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

Complex, find all the 8th roots of (19+7i)

find all the 8th roots of (19+7i)

What is the probability in which the marble chosen is blue, A bag holds 3 r...

A bag holds 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability in which the marble chosen is blue? The probability of blue

What is the smallest possible number 3, What is the smallest possible numbe...

What is the smallest possible number in which can be created along with four decimal places using the numbers 3, 5, 6, and 8? Place the smallest number in the largest place val

Find out the value of n element of a set, A set consists of (2n+1) elements...

A set consists of (2n+1) elements. If the number of subsets of this set which consist of at most n elements is 8192. Find out the value of n. Ans: The following set has (2n + 1

Cylinder, #question Show that the enveloping cylinder of the conicoid ax 2 ...

#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas

Conic sections, The locus of the midpoint of the chords of an ellipse which...

The locus of the midpoint of the chords of an ellipse which are drawn through an end of minor axis is called

Differential Equations, Find the normalized differential equation which has...

Find the normalized differential equation which has { x, xe^x } as its fundamental set

Evaluate the volume of a ball, Evaluate the volume of a ball whose radius i...

Evaluate the volume of a ball whose radius is 4 inches? Round to the nearest inch. (π = 3.14) a. 201 in 3 b. 268 in 3 c. 804 in 3 d. 33 in 3 b. The volume of a

Nonhomogeneous differential equations, Let's here start thinking regarding ...

Let's here start thinking regarding that how to solve nonhomogeneous differential equations.  A second order, linear non-homogeneous differential equation is as y′′ + p (t) y′ +

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