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

Concept, uses of maths concept

uses of maths concept

Compute the probability, From past experience a machine is termed to be set...

From past experience a machine is termed to be set up correctly on 90 percent of occasions.  If the machine is set up correctly then 95 percent of good parts are expected however i

What is the objective of lipids metabolism, What is the objective of lipids...

What is the objective of lipids metabolism ? After studying this unit, you will be able to: 1. explain how fatty acids are oxidized for the production of energy, 2. describe

Union of sets, Union of Sets Venn diagram presenting the union of sets...

Union of Sets Venn diagram presenting the union of sets A and B or A?B = Shaded area is demonstrated below: A ?B = Shaded area

Math, there is 22 owls . my mom gave me 6 more . how many owls do they have...

there is 22 owls . my mom gave me 6 more . how many owls do they have

Root of function, Root of function: All throughout a calculus course we wi...

Root of function: All throughout a calculus course we will be determining roots of functions.  A root of function is number for which the function is zero.  In other terms, determ

Theorem of continuous functions, Consider the subsequent IVP. y' = f(t,y...

Consider the subsequent IVP. y' = f(t,y) ,        y(t 0 ) = y 0 If f(t,y) and ∂f/∂y are continuous functions in several rectangle a o - h o + h which is included in a

Counters and registers, design a synchronous, recycling, MOD-12 counter wit...

design a synchronous, recycling, MOD-12 counter with D FF''s. Use the states 0000 through 1011 in the counter.

Algebra, please tell me what is algebra and how i can understand it

please tell me what is algebra and how i can understand it

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