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

Graphing sets of numbers, Q. Graphing Sets of Numbers? Ans. To  gr...

Q. Graphing Sets of Numbers? Ans. To  graph  a set of numbers on a number line means to plot, or locate, those positions on the line. The number that corresponds to a poin

Shares and dividends, at what price a 6.25%rs 100 share be quoted when the ...

at what price a 6.25%rs 100 share be quoted when the money is worth 5%

Standardizing a random variable, Standardizing a Random Variable       ...

Standardizing a Random Variable       If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

Statistics, How many 4 digit numbers can be formed using the numbers: 1 – 7...

How many 4 digit numbers can be formed using the numbers: 1 – 7. Repeated numbers CAN NOT be used

Polynomials, On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if ...

On dividing p(X)=5x^(4)-4x^(3)+3x^(2)-2x+1 by g(x)=x^(2)+2 if q(x)=ax^(2)+bx+c, find a,b and c.

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