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

Compound interest, you have RM5O,OOO to invest,and two fund that you''d li...

you have RM5O,OOO to invest,and two fund that you''d like to invest in.The You-Risk-It Fund yields 14% interest.The Extra-Dull Fund yields 6% interest.Besause of college financial-

Explain the counting principle in maths, Explain the Counting Principle in ...

Explain the Counting Principle in maths? The fundamental counting principle is used when you want to calculate the total number of possible outcomes (or combinations) of an exp

Arithmetic progressions, ARITHMETIC PROGRESSIONS: One  of the  endlessly a...

ARITHMETIC PROGRESSIONS: One  of the  endlessly alluring  aspects  of mathematics  is  that its thorniest  paradoxes have  a  way  of blooming  into  beautiful  theories Examp

Example of uniform distribution, Q. Samantha wrote a computer program to r...

Q. Samantha wrote a computer program to randomly generate two-digit numbers between 00 and 99. Let X be the random 2 digit number generated by the computer. Find the distributio

Shares and dividends, A man invests rs.10400 in 6%shares at rs.104 and rs.1...

A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all?

Repetition need not be boring-ways to aid learning maths, Repetition Need N...

Repetition Need Not Be Boring :  From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an

Arc length with vector functions - three dimensional space, Arc Length with...

Arc Length with Vector Functions In this part we will recast an old formula into terms of vector functions.  We wish to find out the length of a vector function, r → (t) =

Examples of play and learning maths, Here are a few examples of some team g...

Here are a few examples of some team games. The teams can be small (1-3 children) or big (15-20 children). We start with some games for small children. a) One team places a numb

Right angle triangle, If the points for a right angle triangle are XYZ wher...

If the points for a right angle triangle are XYZ where do I mark the points?

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