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Ratio Test Of A Series

  1. Oct 12, 2012 #1
    1. The problem statement, all variables and given/known data
    I attached a file that includes the author's solution, and some of my work.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Oct 12, 2012 #2

    Mark44

    Staff: Mentor

    The denominator in the series is not (2n + 1)! It is the product of the odd integers from 1 to 2n + 1.
     
  4. Oct 12, 2012 #3
    But can't you write that as (2n + 1)! ?
     
  5. Oct 12, 2012 #4

    Mark44

    Staff: Mentor

    No, not at all.
    (2n + 1)! = 1 * 2 * 3 * ... * (2n - 1) * (2n) * (2n + 1)

    Your expression skips all the even integers.

    A simple example is 5! vs. 1 * 3 * 5. Clearly they aren't equal.
     
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