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

Pre-Calculus, Which point is the reflection through the origin (0, 0) of th...

Which point is the reflection through the origin (0, 0) of the point (-8, -9)?estion..

Explain peano''s axioms with suitable example, Question 1 Explain Peano's ...

Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g

Reduce the rational expression to lowest terms, Reduce the following ration...

Reduce the following rational expression to lowest terms.                                     x 2 - 2 x - 8/ x 2 - 9 x + 20 Solution When reducing a rational expressio

Differentiate outline function in chain rules, Differentiate following. ...

Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2

Determines the possibility, There is a committee to be selected comprising ...

There is a committee to be selected comprising of 5 people from a group of 5 men and 6 women. Whether the selection is randomly done then determines the possibility of having the g

Prove that 2b3-3abc+a2d=0, If  the  ratios  of  the  polynomial ax 3 +3bx...

If  the  ratios  of  the  polynomial ax 3 +3bx 2 +3cx+d  are  in  AP,  Prove  that  2b 3 -3abc+a 2 d=0 Ans: Let p(x) = ax 3 + 3bx 2 + 3cx + d and α , β , r are their three Z

Jordan needs help, carlie is now fivetimes as old as henry. in nine years ...

carlie is now fivetimes as old as henry. in nine years her age will be twice henry''s age then. how old is carly now

Determine the number of blue balls in the bag, A bag contains 5 red balls a...

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball , determine the number of blue balls in the bag.

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