1. Not finding help here? Sign up for a free 30min 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!

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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: PROOF (Sequences & Series); Can anyone help me out?
  1. Can anyone help me? (Replies: 4)

Loading...