Sigma sign in chemistry vs math

[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.

 

[Moo Of Doom]

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

 

[lo2]

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.

 

[Moo Of Doom]

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]

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]

So:
$$\sum_{k=1}^{2} 2k+1=3+5=8$$

Is that right? Or do I lack something?

Yes, that's correct.

 

[Integral]

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]

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.

 

[Data]

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 [itex]...[/tex]'s for!) in terms of $n$ for<br /> <br /> $$\sum_{k=1}^n k.$$<br /> <br /> (where $n$ is a positive integer, of course)[/itex]

 

[lo2]

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 [itex]...[/tex]'s for!) in terms of $n$ for<br /> <br /> $$\sum_{k=1}^n k.$$<br /> <br /> (where $n$ is a positive integer, of course)[/itex]

[itex] <br /> That will be.<br /> <br /> $$\sum_{k=1}^n k.$$=1+(1+1)+...+n-1+n<br /> <br /> Is that right?<br /> <br /> 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. <br /> <br /> Can you then just write.<br /> <br /> $$\sum{H}$$<br /> <br /> Where H just stands instead of something. Do you follow me? If so can you do what I am talking about?[/itex]

 

[Data]

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) .

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 .