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 parallelogram, love is a parallelogram where prove that is a rectangle...

love is a parallelogram where prove that is a rectangle

Algebra, solutions for the equation a-b=5

solutions for the equation a-b=5

How to multiplying monomials, How to Multiplying Monomials? To multiply...

How to Multiplying Monomials? To multiply monomials: Step 1: Multiply the coefficients. Step 2: Multiply the like variables by adding their exponents. Step 3: Multiply ans

Example of function, Example  Suppose the demand and cost functio...

Example  Suppose the demand and cost functions are given by          Q = 21 - 0.1P and C = 200 + 10Q Where,          Q - Quantity sold

Unit vector and zero vectors, Unit Vector and Zero Vectors Unit Vec...

Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (

Multiple, what number does not belong 43,47,53,59,65,67

what number does not belong 43,47,53,59,65,67

Need answer urgently, using a pair of compasses a ruler and a pencil. const...

using a pair of compasses a ruler and a pencil. construct a triangle CDE in which DE=10cm, DC+8cm and CDE= 45 degrees. construct CF perpendicular to DE such that F lies on DE using

Describe about arithmetic and geometric series, Describe about Arithmetic a...

Describe about Arithmetic and Geometric Series? When the terms of a sequence are added together instead of separated by commas, the sequence becomes a series. You will use seri

Detemine the amplitude of trigonometric function, 1. Consider the trigonome...

1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by

Solid mensuration, what is the importance of solid mensuration?

what is the importance of solid mensuration?

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