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Help! Factorial Partial Fraction Decomposition

  • Thread starter danerape
  • Start date
  • #1
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Homework Statement



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
 

Answers and Replies

  • #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]
 
  • #3
dextercioby
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n/(n+1)!= 1/n! - 1/(n+1)!
 
  • #4
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Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!
 
  • #5
dextercioby
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It's easy to prove. In the LHS write n=(n+1)-1.
 
  • #6
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Wow, that is pretty obvious, I haven't had any experiance with ! before this though. Thanks alot!!!!

Dane
 

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