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MacLaurin Series help

  1. Apr 14, 2013 #1
    1. The problem statement, all variables and given/known data

    "Find the sum of the seires:

    3 + (9/2!) + 27/3! +81/4!+ .... "


    2. Relevant equations



    e^x = Ʃ n=0 to inf (x^n)/n!




    3. The attempt at a solution
    =3(1 +3/2! + 9/3! + 27/4! + ...
    =3*Ʃ n=0 to inf( (3^n)/(n+1)!)
    =Ʃ n=0 to inf( (3^(n+1))/(n+1)!)

    . unsure what to do from here, maybe break apart the sigma by re-indexing? Im not sure how to do this. Any help would be greatly appreciated.
     
  2. jcsd
  3. Apr 14, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Why did you pull out the 3? If you are missing the first term, I would add it manually in the sum (and subtract it outside). This is easier than an index shift.
     
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