1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

McLaurin series

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    Given a McLauren series: (2x)^n+1 / (n+1)

    (a). Find interval of convergence.

    2. Relevant equations

    Limit test

    3. The attempt at a solution

    So I used ratio test and found that -1/2 <x<1/2. I am testing the end point. At x=1/2, the series will be 1/(n+1) and at x=-1/2, series is (-1)^n+1 / (n+1). How do I prove whether or not they are divergent or convergent. Does 1/ (n+1) converge to 0 ?

    How about when x=-1/2, is it convergent or divergent ?
     
  2. jcsd
  3. Mar 30, 2009 #2
    I imagine you forgot to put the summation notation before your terms?? McLaurin series are infinite summations; anyways, 1/(n+1) converges to 0, but this is not sufficient to prove that it converges. Can you think of a fairly famous series that this reminds you of?? Similarly for the Alternating Series at x=(-1/2); although for the alternating series you could also use the alternating series test.
     
  4. Mar 31, 2009 #3
    Do I compare 1/(n+1) to 1/n ??
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook