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

Limit, limit x APProaches infinity (1+1/x)x=e

limit x APProaches infinity (1+1/x)x=e

The fisher’s index, The Fisher's index The index of Fisher acts as a c...

The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.

Estimate the total cost of the books, Frederick bought six books which cost...

Frederick bought six books which cost d dollars each. What is the total cost of the books? Frederick would multiply the number of books, 6, through how much each one costs, d.

base - 10 block math, there are 5 small cubes and it reads the 5 small cub...

there are 5 small cubes and it reads the 5 small cubes is 1/100, then what is the ONE?

Eigenvalues and eigenvectors, Review: Systems of Equations - The tradition...

Review: Systems of Equations - The traditional initial point for a linear algebra class. We will utilize linear algebra techniques to solve a system of equations. Review: Matr

Mean roots, Find all the eighth roots of (19 + 7 i)

Find all the eighth roots of (19 + 7 i)

Sin3? = cos2? find the most general values of ?, sin3θ = cos2θ find the mos...

sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution)  sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(

Multiplying fractions involving negative numbers, Q. Multiplying Fractions ...

Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe

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