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Homework Help: PROOF (Sequences & Series); Can anyone help me out?

  1. Jan 28, 2008 #1
    Prove that:
    ∀ n€N [(the) sum of an (infinite?) series (a1,+a2,...+,an)] (where [tex]a_{n}[/tex]=[tex]\frac{n}{(n+1)!}[/tex])
    [tex]\sum \frac{n}{(n+1)!}[/tex] (is equal to/gives/yields) = 1 - [tex]\frac{1}{(n+1)!}[/tex]

    Prove that:
    ∀ n [tex]\in[/tex] N [tex]\sum \frac{n}{(n+1)!}[/tex] = 1 - [tex]\frac{1}{(n+1)!}[/tex]

    THX in advance
     
  2. jcsd
  3. Jan 28, 2008 #2

    EnumaElish

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    What is the summation index?
     
  4. Jan 28, 2008 #3
    how it can be
    [tex]\sum\frac{n}{n+1!}[/tex]=[tex]\sum\frac{1}{n!}\frac{1}{n+1!}[/tex]
    there is a negative sign between last two expessions in n
    e-1-(e-2)=1
     
    Last edited: Jan 28, 2008
  5. Jan 30, 2008 #4
    Hey there,

    A possible derivation of the sum requested uses the telescoping series property.
    Note that for every j, Aj can be expended to -

    Aj = j / ( j + 1 )! = 1 / j! - 1 / ( j + 1)!

    Summing over 1,...,n would then yield the desired result.
     
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