# Sigma sign

lo2
Hi there,

We are about to use that sigma sign in chemistry we have however not got told about it in math. SO therefore I am asking you if you could give me a brief introduction to it and how to use it and etc.

The capital sigma? Like $$\sum_{k=1}^{n} 2k+1$$?

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lo2
Moo Of Doom said:
The capital sigma? Like $$\sum_{k=1}^{n} 2k+1$$?
Yeah precisly I am sorry for not being more precise. I know that it has something to do with the sum of something but I do not really know the details which I also would like to know.

Well, $$\sum_{k=a}^b f(k) = f(a) + f(a+1) + f(a+2) + ... + f(b-1) + f(b)$$. Usually a will be 0 or 1, but it doesn't have to.

lo2
Moo Of Doom said:
The capital sigma? Like $$\sum_{k=1}^{n} 2k+1$$?
So:
$$\sum_{k=1}^{2} 2k+1=3+5=8$$

Is that right? Or do I lack something?

HallsofIvy
Homework Helper
lo2 said:
So:
$$\sum_{k=1}^{2} 2k+1=3+5=8$$

Is that right? Or do I lack something?
Yes, that's correct.

Integral
Staff Emeritus
Gold Member
First off you need to know a bit about how the notation works:

$$\sum_{k=1}^{5} k$$

This is a very explicit example.

Notice the k=1 under the sigma, k is called the index, 1 is the start value. The number (5 in this case) or symbol above the sigma is the end value of the index. To expand the notation, replace the index in the expression after the sigma (k in this case) first with the start value (1) then increment the index by 1 and repeat. So the expression above becomes

1+2+3+4+5

It is really pretty easy.

lo2
Integral said:
First off you need to know a bit about how the notation works:

$$\sum_{k=1}^{5} k$$

This is a very explicit example.

Notice the k=1 under the sigma, k is called the index, 1 is the start value. The number (5 in this case) or symbol above the sigma is the end value of the index. To expand the notation, replace the index in the expression after the sigma (k in this case) first with the start value (1) then increment the index by 1 and repeat. So the expression above becomes

1+2+3+4+5

It is really pretty easy.
Yeah well, I think that a bit of excercise would be good. I mean you first really learn something when you try it and try to use it. In other words it is learning by doing.

Well, you can come up with your own problems pretty easily. Now that you know what the notation means, you could try this one:

Find a closed form (ie. not including any "sigma" notation, or any sums you need to use $...[/tex]'s for!) in terms of [itex]n$ for

$$\sum_{k=1}^n k.$$

(where $n$ is a positive integer, of course)

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lo2
Data said:
Well, you can come up with your own problems pretty easily. Now that you know what the notation means, you could try this one:

Find a closed form (ie. not including any "sigma" notation, or any sums you need to use $...[/tex]'s for!) in terms of [itex]n$ for

$$\sum_{k=1}^n k.$$

(where $n$ is a positive integer, of course)
That will be.

$$\sum_{k=1}^n k.$$=1+(1+1)+...+n-1+n

Is that right?

Else if you want to like get the sum of something it can be a formula where you have to add something, some diffrent numbers.

Can you then just write.

$$\sum{H}$$

Where H just stands instead of something. Do you follow me? If so can you do what I am talking about?

Well, you needed to use a "...", so that's not quite what I meant (see if you can find an easy-to-evaluate formula for it that works for any positive integer $n$, without "..."'s) :tongue2:.

As to your question, often people (especially in physics) will use the notation without stating the indices of notation. And indeed, it is perfectly legitimate to sum over sets of any type. But it's usually good to indicate exactly what set you are summing over .