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

Terminology of polynomial, Terminology of polynomial Next we need to ge...

Terminology of polynomial Next we need to get some terminology out of the way. Monomial polynomial A monomial is a polynomial which consists of exactly one term.

Speed, Town x and town y were 270km apart. a car started from town x toward...

Town x and town y were 270km apart. a car started from town x towards town y at a uniform speed of 60km/hr, while a motorcycle started from town y to town x at a uniform speed of 9

Find the limit of given matrix, What is required: This assignment is to be ...

What is required: This assignment is to be resolved using Maple. You are to upload a single Maple worksheet with file name FamilynameFirstname.mw (e.g., CarrElliot.mw), using the A

Substitution rule, Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (...

Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du,     where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably

What are the three sides of a right triangle, What are the Three Sides of a...

What are the Three Sides of a Right Triangle? Each side of a right triangle can be labeled opposite, adjacent, or hypotenuse, based on its relationship to the right angle and o

If all the tickets are the similar price what was the cost, The total ticke...

The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale

Arithmetic progression., 1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d ar...

1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d are in A.P 2.The nth term of an A.P is an+b.Find the sum of the series upto n terms.

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