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Help! Factorial Partial Fraction Decomposition

  1. Nov 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Show that n/(n+1)!=(1/n)-(1/(n+1)!)

    I am totally lost on the algebraic steps taken to come to this conclusion. It is for an
    Infinite series.

    Thanks
     
  2. jcsd
  3. Nov 21, 2011 #2

    vela

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    It's not true. For example, take n=3. Then
    [tex]\frac{n}{(n+1)!} = \frac{3}{4!} = \frac{3}{24} = \frac{1}{8}[/tex]but
    [tex]\frac{1}{n}-\frac{1}{(n+1)!} = \frac{1}{3}-\frac{1}{24} = \frac{8}{24}-\frac{1}{24} = \frac{7}{24}[/tex]
     
  4. Nov 21, 2011 #3

    dextercioby

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    n/(n+1)!= 1/n! - 1/(n+1)!
     
  5. Nov 21, 2011 #4
    Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!
     
  6. Nov 21, 2011 #5

    dextercioby

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    It's easy to prove. In the LHS write n=(n+1)-1.
     
  7. Nov 21, 2011 #6
    Wow, that is pretty obvious, I haven't had any experiance with ! before this though. Thanks alot!!!!

    Dane
     
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