Calculus

posted by .

I'm studying infinite series and am really struggling with memorizing all the tests for convergence in my book, there's like 10 of them. I don't think I'm going to be successful in memorizing all of them. I will never be asked in my course to use a specific test to determine convergence but to determine weather a series converges using a test and showing my work.

I'm really afraid that on my examinations there are going to be series were the only way I can evaluate them is by using one test only, one that I learned that is, or that I'm going to get my examination and see a question that asks me to determines weather or not a infinite series converges or not, and my mind will just go blank as I go through all the tests that I know in my head, which will be hard to do when I don't really have them all memorized...

So I was wondering if someone could inform me of the be all end all test for convergence for infinite series, that can be used for any infinite series, or most of them. I wouldn't mind spending some time learning something new, if I can just really get the one technique down and master it. There's got to be some test that can be done on all series, or most of them, that's in some upper math courses that I haven't studied yet.

  • Calculus -

    The problem here is that a method that always works is usually less efficient. The tests for convergence can all be derived from first principles using the rigorous definition of a limit.

    The best thing you can do is to study the derivation of all the tests and also to solve some problems without using any of the standard test from first principles. You'll then get a better feeling of when to apply which test.


    The general method that is practical for summations is to use the Cauchy property. So a series converges if and only if for every epsilon > 0 there exists an N such that for all n and m larger than N, the absolute value of the summation from n to m is less than epsilon.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY?
  2. calculus-- need help desperately!

    The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by f^(n) (5)= (-1)^n(n!)/((2^n)(n+2)), and f(5)=1/2. Write third degree Taylor …
  3. calculus

    I'm studying for a quiz on infinite series and convergence/divergence tests. I keep getting confused between the variables "k" and "n". What is the difference between the two?
  4. social studies

    My child is having problem memorizing the dates related to the battles and establishments of kingdoms.so was browsing to find methods to help him improve his memory,came across a site funnelbrain which provides a collaborative platform …
  5. Calculus

    a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of …
  6. Calculus

    What is the radius of convergence of the power series (((2n)!x^(n))/((2n-1)!)), and what is its interval of convergence?
  7. VERY SMALL QUESTION

    I'm having trouble memorizing my French vocabulary, so I decided to record my voice saying all the words and their meanings and then playing them over on my headphones. Is this is a good way of memorizing, will it help?
  8. Small question memorizing help

    I'm having trouble memorizing my French vocabulary, so I decided to record my voice saying all the words and their meanings and then playing them over on my headphones. Is this is a good way of memorizing, will it help?
  9. calculus

    in the following series x is a real number. In each case use the ratio test to determine the radius of convergence of the series. Analyze the behavior of the series at the endpoints in order to determine the interval of convergence. …
  10. writing

    We also prepared for the test by studying the driver's booklet, memorizing rules, and to learn road signs. What correction should be made to this sentence?

More Similar Questions