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

how many of the original vectors, We have claimed that a randomly generate...

We have claimed that a randomly generated point lies on the equator of the sphere  independent of where we pick the North Pole.  To test this claim randomly generate ten  vectors i

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

Minimum and maximum values, Minimum and Maximum Values : Several applicati...

Minimum and Maximum Values : Several applications in this chapter will revolve around minimum & maximum values of a function.  Whereas we can all visualize the minimum & maximum v

General math, Kwai made 5 pints of iced tea. How many cups of tea did he ma...

Kwai made 5 pints of iced tea. How many cups of tea did he make?

Negative number, what should added to the sum of (-26) and 31 to m...

what should added to the sum of (-26) and 31 to make it equal to the sum of (-35) and (-11) question #Minimum 100 words accepted#

Equation of the line which passes through the two points, Example: Write do...

Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5). Solution At first glance it might not appear which we'll be capable to

Determine the relative global error, Consider the differential equation giv...

Consider the differential equation give by y′ = -10(y - sin t) (a) Derive by hand exact solution that satis?es the initial condition y(0) = 1. (b) Numerically obtain the s

Linear programming, Consider the following linear programming problem: M...

Consider the following linear programming problem: Min (12x 1 +18x 2 )             X 1 + 2x 2 ≤ 40             X 1 ≤ 50             X 1 + X 2 = 40             X

5% sales tax on a basket what was the price of the basket, The 5% sales tax...

The 5% sales tax on a basket was $0.70. What was the price of the basket? Use a proportion to solve the problem; part/whole = %/100. The whole is the price of the basket (wh

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