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

Group automorphism, (a) Find an example of groups G, H, K with K  H and H...

(a) Find an example of groups G, H, K with K  H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve

Profit, A wholesaler allows a discount of 20% on the list price to a retail...

A wholesaler allows a discount of 20% on the list price to a retailer. The retailer sells at 5% discount on the list price.If a customer paid Rs 114 for an article,what profit is m

Operations and properties, use an expression to write an expression with fi...

use an expression to write an expression with five 3s that has a value of 0

MENSURATION, HOW TO FIND THE HEIGHT OF A CYLINDER I NEED IT FOR ASSIGNMENT ...

HOW TO FIND THE HEIGHT OF A CYLINDER I NEED IT FOR ASSIGNMENT TO BE SUBMITTED BY 8;00 AM

Trigonometry, A 25 foot ladder just reaches the top of a house and forms an...

A 25 foot ladder just reaches the top of a house and forms an angle of 41.5 degrees with the wall of the house. How tall is the house?

Circle, prove that - there is one and only one circle passing through three...

prove that - there is one and only one circle passing through three non - collinear points

Sketch a graph of the microphone signal, Figure shows noise results for a p...

Figure shows noise results for a prototype van measured on a rolling road. The vehicle had a four-cylinder-in-line engine. The engine speed was varied in 3rd gear from just above

Perimeter and Area, A farmer has a rectangular field of length 100m and bre...

A farmer has a rectangular field of length 100m and breadth 70m. He leaves a path of 1m all along the boundary inside it. He decides to apply a manure to the remaining part of the

Quadratic Equation, Short Cuts for solving quadratic equations

Short Cuts for solving quadratic equations

Derivatives of hyperbolic functions , Derivatives of Hyperbolic Functions ...

Derivatives of Hyperbolic Functions : The last set of functions which we're going to be looking at is the hyperbolic functions.  In several physical situations combinations of e

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