1. Limited time only! Sign up for a free 30min personal 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!

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


    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


    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


    User Avatar
    Homework Helper

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


    [tex]\left[ (n+1)!\right]^2 = \left[ (n+1)\times n!\right]^2[/tex]
  6. May 20, 2015 #5
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook