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

Explain the algebraic expressions and equations, Explain the Algebraic Expr...

Explain the Algebraic Expressions and Equations? Writing a math problem algebraically means that you are using numbers and variables to represent relationships. "Three inche

Differential equation, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

MUTIPLYING FRACTIONS, EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MUL...

EVERY TIME I TRY TO DO ANY KIND OF FRACTIONS WELL MULTIPLYING I ALWAYS GET IT WRONG

What is this distance expressed in standard notation, The distance from the...

The distance from the sun to the earth is approximately 9.3 × 10 7 miles. What is this distance expressed in standard notation? In order to convert this number to standard not

Draw the graph for finite state machine, Consider the finite state machine ...

Consider the finite state machine whose state transition table is : Draw the graph for it.  Ans: The graph for the automata according to the transition table is drawn b

Calculus, I need help with my calculus work

I need help with my calculus work

What difference among the areas of the two sections of a, If the areas of t...

If the areas of two sections of a garden are 6a + 2 and 5a, what is the difference among the areas of the two sections within terms of a? Because the question asks for the diff

Working definition of function, A function is an equation for which any x w...

A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w

Explain simple classification and chance and probability, E1) From your exp...

E1) From your experience, and what you have studied so far, by which age would-you expect an average child to be ready to acquire the following concepts? i) Simple classificatio

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