Homework Help: Sigma notation of a series.

1. Feb 8, 2008

Seda

[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. Feb 8, 2008

quasar987

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

$$\sum_{i=1}^n a_i$$

This being said, can you answer your question now?

3. Feb 8, 2008

Gib Z

And your formula is incorrect by the way. Its $$\frac{n(n+1)}{2}$$.

4. Feb 8, 2008

Seda

Well, that's how the problem was listed in by homework....

hmm, I guess I'll answer it "false" then.....

5. Feb 8, 2008

Gib Z

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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