Absolute convergence - sequences and series, Mathematics

Assignment Help:

Absolute Convergence

While we first talked about series convergence we in brief mentioned a stronger type of convergence but did not do anything with it as we didn't have any tools at our disposal which we could make use of to work problems involving it.  Now we have some of those tools thus it's now time to talk about absolute convergence in detail.

1st, let's go back over the definition of absolute convergence.

A series ∑an is termed as absolutely convergent if ∑|an| is convergent. If ∑an is convergent and ∑|an| is divergent this known as the series conditionally convergent. We as well have the following fact about absolute convergence.

 


Related Discussions:- Absolute convergence - sequences and series

Utilize the chain rule to differentiate, Chain Rule : Assume that we have ...

Chain Rule : Assume that we have two functions f(x) & g(x) and they both are differentiable. 1.   If we define F ( x ) = ( f o g ) ( x ) then the derivative of F(x) is,

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.

Give the example of exponents, Give the example of Exponents? When a nu...

Give the example of Exponents? When a number is multiplied several times, it is easier to write it as an exponent. For example, four multiplied to itself three times, is writte

Probabillity, In my wallet there is a 10p stamp, a 12p stamp and a 20p stam...

In my wallet there is a 10p stamp, a 12p stamp and a 20p stamp.I remove a stamp,put it back and then remove a stamp again.Draw a sample space diagram to show all the possible resul

Find the solution to initial value problem, Illustration:   Find the soluti...

Illustration:   Find the solution to the subsequent IVP. ty' + 2y = t 2 - t + 1,      y(1) = ½ Solution : Initially divide via the t to find the differential equation in

How much does it car cost her per year, Ashley's car insurance costs her $1...

Ashley's car insurance costs her $115 per month. How much does it cost her per year? Multiply $115 by 12 because there are 12 months in a year; $115 × $12 = $1,380 per year.

In an election contested between a and b determine vote, In an election con...

In an election contested between A and B, A obtained votes equal to twice the no. of persons on the electoral roll who did not cast their votes & this later number was equal to twi

Childrens errors are a natural and inevitable part, Childrens errors are a ...

Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may

Distribution of sample distribution or sampling means , Distribution of Sam...

Distribution of Sample distribution or Sampling means A sample of size n is taken from the parent population and mean of the sample is estimated. It is repeated for a number o

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