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Sigma notation of a series.

  1. Feb 8, 2008 #1
    [SOLVED] Sigma notation of a series.

    I have the formula

    1+2+3+...+n = (n^2+n+1)/2,

    and I thinkthat this is the formula for the sum of a series. I need to write this thing in sigma notation, and then prove it by induction. I'm usually good and proving things by induction, but I can't even figure out how to get this thing into sigma notation!

    I think by pluging in values that this series is 3/2 + 2 + 3 + 4 + 5 + etc

    This seems like it should be easy, but wow I have been stumped for awhile. Help is appreciated.
     
    Last edited: Feb 8, 2008
  2. jcsd
  3. Feb 8, 2008 #2

    quasar987

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    This is how it works formally.

    If you are given a list of numbers {a_1, a_2, a_3,..., a_n} and you consider their sum a_1 + a_2 + ... + a_n, then we write this is sigma notation as

    [tex]\sum_{i=1}^n a_i[/tex]

    This being said, can you answer your question now?
     
  4. Feb 8, 2008 #3

    Gib Z

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    And your formula is incorrect by the way. Its [tex]\frac{n(n+1)}{2}[/tex].
     
  5. Feb 8, 2008 #4
    Well, that's how the problem was listed in by homework....

    hmm, I guess I'll answer it "false" then.....
     
  6. Feb 8, 2008 #5

    Gib Z

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    I guess if u want extra credit, show the original statement is false, eg if you let n=1, it states 1 = 3/2. Then give them the right expression and then prove that one =]
     
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