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

Correlation and regression, Correlation and Regression Correlation ...

Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of

Math, what is 24566x12567=

what is 24566x12567=

Differential equation, Verify Liouville''''s formula for y "-y" - y'''' + y...

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)

Series is converges or diverges - limit comparison test, Determine if the f...

Determine if the following series converges or diverges by using limit comparison test. Solution To make use of the limit comparison test we require to find out a seco

Math, there is 22 owls . my mom gave me 6 more . how many owls do they have...

there is 22 owls . my mom gave me 6 more . how many owls do they have

Simple harmonic motion, prove that the composition of two simple harmonic o...

prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.

Find the greatest number of 6 digits exactly divisible by 24, Find the grea...

Find the greatest number of 6 digits exactly divisible by 24, 15 and 36. (Ans:999720) Ans: LCM of 24, 15, 36 LCM = 3 × 2 × 2 × 2 × 3 × 5 = 360 Now, the greatest six digit

How many pounds should nicole put in every basket, Nicole is forming 20 gif...

Nicole is forming 20 gift baskets. She has 15 pounds of chocolates to distribute equally between the baskets. If each basket gets the similar amount of chocolates, how many pounds

theoretical minimum number of stations, A company is setting up an assembl...

A company is setting up an assembly line to produce 100 units/hour. The table shown below identifies the work elements, times, and immediate predecessors. a)      What cycle tim

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