Alternating series test - sequences and series, Mathematics

Assignment Help:

Alternating Series Test - Sequences and Series

The final two tests that we looked at for series convergence has needed that all the terms in the series be positive.  Actually there are several series out there that have negative terms in them and thus we now need to start looking at tests for these types of series.

The test which we are going to look into in this part will be a test for alternating series.  An alternating series is some series, ∑an , for that the series terms can be written in one of the subsequent two forms.

an = (-1)n bn                                       bn > 0

an = (-1)n+1 bn                                             bn > 0

There are so many other ways to deal with the alternating sign, although they can all be written as one of the above two forms.  For illustration,

(-1)n+2 = (-1)n (-1)2 = (-1)n

(-1)n+1 ­= (-1)n+1 (-1)-2 = (-1)n+!

Certainly there are many others, but they all follow similar basic pattern of reducing to one of the first two forms that given.  If you should happen to run into a dissimilar form than the first two, don't worry about transforming it to one of those forms, just be alert that it can be and thus the test from this section can be used.


Related Discussions:- Alternating series test - sequences and series

Fractions, how do i multiply and divide fractions?

how do i multiply and divide fractions?

Example of developing an understanding, In class 1, the teacher had written...

In class 1, the teacher had written down the digits 0,1, ...., 9 on the board. Then she made all the children recite the corresponding number names. Finally, she made them write th

Probability, An unbiased die is tossed twice .Find the probability of getti...

An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss

People fit, How many people ca fi in a small cars without seats?

How many people ca fi in a small cars without seats?

Project, report on shares and dovidend using newspaer

report on shares and dovidend using newspaer

Factors, write down all the factors of 36

write down all the factors of 36

How far is balloon from the shore, Steve Fossett is going the shores of Aus...

Steve Fossett is going the shores of Australia on the ?rst successful solo hot air balloon ride around the world. His balloon, the Bud Light Spirit of Freedom, is being escorted

What is a mixed number, Q. What is a Mixed Number? Ans. A mixed nu...

Q. What is a Mixed Number? Ans. A mixed number is an integer, along with a fractional part, which has the same sign. (Therefore, a mixed number always has two parts.) M

Find out the volume of the solid -y = (x -1) ( x - 3)2, Find out the volume...

Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r

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