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

What do you mean by transient state, What do you mean by transient state an...

What do you mean by transient state and steady-state queueing systems If the characteristics of a queuing system are independent of time or equivalently if the behaviour of the

Example of factor by grouping, Factor by grouping each of the following. ...

Factor by grouping each of the following. 3x 2 - 2x + 12x - 8 Solution           3x 2 - 2x + 12x - 8 In this case we collect the first two terms & the final two te

Pemdas, 15(4*4*4*4*+5*5*5)+(13*13*13+3*3*3)

15(4*4*4*4*+5*5*5)+(13*13*13+3*3*3)

Example of graphing equations, Example of Graphing Equations: Example...

Example of Graphing Equations: Example: By using the above figure, find out the distance traveled if the average speed is 20 mph and the time traveled is 40 minutes. T

Transpotation, how can you determine trasportation schedule that minimizes ...

how can you determine trasportation schedule that minimizes cost

Basics of vectors - calculus, Vectors - The Basics Let us start this s...

Vectors - The Basics Let us start this section off with a quick discussion on what is the use of vector.  Vectors are utilized to present quantities that have both a magnitude

Find the length and breadth of the rectangle, The area of a rectangle gets ...

The area of a rectangle gets decreased by 8 m2, if its length  is decreased by 5 m and breadth increased by 3 m. If we enhance  the length by 3 m and breadth by 2 m, the area is en

Projectile, what is the greatest projection range down an inclined plane? h...

what is the greatest projection range down an inclined plane? how we will calculate that?

Factoring trinomial, what is the factor of the trinomial 2x2-7x-4

what is the factor of the trinomial 2x2-7x-4

Estimate the slope of a line?, Estimate the Slope of a Line? The slope o...

Estimate the Slope of a Line? The slope of a line is a measure of how steep it is. It is defined as y 2 - y 1 /x 2 -x 1 Where (x 1 , y 1 ) and (x 2 , y 2 ) are any two p

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