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

Finding absolute extrema, Finding Absolute Extrema : Now it's time to see ...

Finding Absolute Extrema : Now it's time to see our first major application of derivatives.  Specified a continuous function, f(x), on an interval [a,b] we desire to find out the

Three whole divisions, In the National Hockey championship, there are 30 in...

In the National Hockey championship, there are 30 independent ice hockey teams. Every of the teams will play 82 official NHL games every year. Many teams will have to travel from t

Help with word problem, You would like to have $4000 in four years for a sp...

You would like to have $4000 in four years for a special vacation following graduation by making deposits at the end of every 6 months in an annuity that pays 7% compounded semiann

Example of division of fractions, Example of division of fractions: E...

Example of division of fractions: Example: (4/5)/(2/9) = Solution: Step 1:             Invert the divisor fraction (2/9) to (9/2). Step 2:             Multip

Number theory, formula for non negative solutions integral

formula for non negative solutions integral

Extrema- minimum and maximum values, Extrema : Note as well that while we ...

Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,

BOUNDARY VALUE PROBLEM, Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0...

Ut=Uxx+A exp(-bx) u(x,0)=A/b^2(1-exp(-bx)) u(0,t)=0 u(1,t)=-A/b^2 exp(-b)

Statewide mortality rates, Assume that between workers exposed to asbestos ...

Assume that between workers exposed to asbestos in a shipyard in 1980, 33 died over a 10 year period from COPD, whereas only 24 such deaths would be expected based on statewide mor

Ratio lanquage, Alexis needs to paint the four exterior walls of a large re...

Alexis needs to paint the four exterior walls of a large rectangular barn. the length of the barn is 80 feet the width is 50 feet and the height is 30 feet. The pain costs 28 dolla

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