Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Determine the interval of convergence for

  1. Apr 29, 2010 #1
    1. The problem statement, all variables and given/known data

    [n=0 to ∞] ∑x2n/n!

    2. Relevant equations

    The ratio test

    3. The attempt at a solution

    So, here is the ratio of of the (n+1)th term to the nth term:

    | [x2(n+1)/(n+1)!] / [x2n/n!] | =

    | [x2nx2/(n+1)!] * [n!/x2n] | =

    | x2/n |, which will be will be less than one when n is big enough.

    So this converges for all x, right?
     
  2. jcsd
  3. Apr 29, 2010 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Correct.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook