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

Find the z-score, For a population with a mean of μ=80 and a standard devia...

For a population with a mean of μ=80 and a standard deviation of o=12, find the z-score corresponding to each of the following samples. a.    M=83 for a sample of n=4 scores b.

Cirlce Division, How can i calculate arc length for dividing a circle into ...

How can i calculate arc length for dividing a circle into 10 parts

Comparison test - sequences and series, Comparison Test Assume that we...

Comparison Test Assume that we have two types of series ∑a n and ∑b n with a n , b n ≥ 0 for all n and a n ≤ b n for all n.  Then, A.  If ∑b n is convergent then t

Mathematics Logic & Set Applications, I have a 40 question assignment for t...

I have a 40 question assignment for this topic, will you be able to complete it?

Using pythagorean theorem to determine z, Two cars begin 500 miles apart.  ...

Two cars begin 500 miles apart.  Car A is into the west of Car B and begin driving to the east (that means towards Car B) at 35 mph & at the similar time Car B begin driving south

Compute the volume and surface area of a right circular cone, Compute the v...

Compute the volume and surface area of a right circular cone: Compute the volume and surface area of a right circular cone along with r =  3", h = 4", and l = 5".  Be sure to

Answer, #questi0+50x1-60-60x0+10on..

#questi0+50x1-60-60x0+10on..

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