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

The mean value theorem for integrals of even and odd , The Mean Value Theor...

The Mean Value Theorem for Integrals If  f (x ) is a continuous function on [a,b] then there is a number c in [a,b] such as,                                    ∫ b a f ( x

Multiplication and division , In multiplication and division we have 1) ...

In multiplication and division we have 1) Suggested ways of conveying the meaning of multiplication and division to children. These operations have to be taught as an activit

Direct and inverse variation, A man can do a piece of work in 25 days how m...

A man can do a piece of work in 25 days how many people are required to complete same work in 15 days?

Give the proofs in mathematics, Give the Proofs in Mathematics ? 1 Two...

Give the Proofs in Mathematics ? 1 Two-column deductive proof Proof: Statements                                                              Reasons * Start with given c

Calculate the volume and surface area of a sphere, Calculate the volume and...

Calculate the volume and surface area of a sphere: Calculate the volume and surface area of a sphere with r = 4".  Be sure to include units in your answer. Solution: V

Geometry, RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS...

RS=8y+4 ST=4y+8 RT=15y-9 a.) WHAT IS THE VALUE OF y b.) FIND RS, ST, AND RT

Items price list, what is the unit price of 6.5 cups of pizza sauce?

what is the unit price of 6.5 cups of pizza sauce?

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