How can I write the sum of a series in sigma notation and prove it by induction?

[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.

 

[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?

 

[Gib Z]

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

 

[Seda]

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

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

 

[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 =]