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Sum this series

  1. Nov 22, 2012 #1

    utkarshakash

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    Gold Member

    1. The problem statement, all variables and given/known data
    1.1!+2.2!+3.3!.......n terms

    2. Relevant equations

    3. The attempt at a solution
    The first part of every term is in AP whose cd is 1. Also the nth term of this series is given as n.n! If I expand it it becomes n.n(n-1)(n-2).......1

    Now
    [itex]S_n=\sum t_n \\
    = \sum n.n(n-1)(n-2)......1 [/itex]

    But now how do I compute this summation?
     
  2. jcsd
  3. Nov 22, 2012 #2

    Mentallic

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    Consider n = (n+1)-1
     
  4. Nov 22, 2012 #3

    utkarshakash

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    I didn't get you. What you said was to replace all the n's with (n+1)-1 but I didn't find it to be helpful. Can you please give me some more hints?
     
  5. Nov 22, 2012 #4

    Mentallic

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    Not all n's!

    n.n! = [(n+1)-1]n!
     
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