1. Nov 21, 2011 #1

   danerape

   

   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

    

   danerape, Nov 21, 2011
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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]

    

   vela, Nov 21, 2011
4. Nov 21, 2011 #3

   dextercioby

   

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

    

   dextercioby, Nov 21, 2011
5. Nov 21, 2011 #4

   danerape

   

   Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!

    

   danerape, Nov 21, 2011
6. Nov 21, 2011 #5

   dextercioby

   

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   It's easy to prove. In the LHS write n=(n+1)-1.

    

   dextercioby, Nov 21, 2011
7. Nov 21, 2011 #6

   danerape

   

   Wow, that is pretty obvious, I haven't had any experiance with ! before this though. Thanks alot!!!!
   
   Dane

    

   danerape, Nov 21, 2011

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