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How to manipulate factorials

  1. May 19, 2015 #1
    I have been practicing power series problems and a lot of them include factorials. To find out if they converge or not I'll often use the ratio test. However, I never quite understood how to cancel factorials when replacing the n with n+1. i.e. the textbook has an example problem that shows that

    [(n+1)!]2 ⇒ (n+1)2 (n!)

    How is this done?

    Thank you in advance.
     
  2. jcsd
  3. May 19, 2015 #2

    Mark44

    Staff: Mentor

    In your example, [(n+1)!]2 means [(n+1)!] * [(n+1)!], which would be (n + 1)2(n)2(n - 1)2 ... 3222.
     
  4. May 19, 2015 #3

    statdad

    User Avatar
    Homework Helper

    Note that [itex] [(n+1)!]^2 \ne \big(n+1\big)^2 \big(n!\big) [/itex], so you will have difficulty reducing the left side to the right side. :)
     
  5. May 19, 2015 #4

    Mentallic

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    Homework Helper

    A slight typo, but it should be
    [tex](n+1)! = (n+1)\times n![/tex]

    Hence

    [tex]\left[ (n+1)!\right]^2 = \left[ (n+1)\times n!\right]^2[/tex]
     
  6. May 20, 2015 #5
    Thanks
     
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