# Quick question on sums

1. Nov 4, 2004

### Fert

If I have a problem like
(N) sigma (K=0) Cos(Kpi)

Cos(pi Sigma K)

just wondering because I have this on an assignment problem and we didn't learn it in class and the text book doesn't cover it either. If I can move it inside the answer is easy so I am just assuming thats how to do it.

Also, how do you guys write all the math symbols, etc. I see them in other posts but I am pretty much useless on a computer so I have no idea how to do it.

Thanks

2. Nov 4, 2004

### James R

No, you can't just move it inside. For example, consider:

$$\sum\limits_{k=1}^3 \cos(k\pi) = \cos(\pi) + \cos(2\pi) + \cos(3\pi)$$

whereas

$$\cos(\pi \sum\limits_{k=1}^3 k) = \cos(\pi(1 + 2 + 3)) = \cos(6\pi)$$

These are not the same thing.

(To see how the maths was displayed, click on the displayed equations.)

3. Nov 4, 2004

### Fert

Yeah, I see what your saying. I tried it out after I posted. The problem is I don't have an end number to evaluate it at, but I have a formula for $$\sum\ limits_{K=0}^n K$$. I'm thinking because there is no no number to evaluate it at that the answer is just a general formula, like n(n+1)/2 but our text book desn't cover it and we didn't take it in class.

4. Nov 4, 2004

### Fert

sorry about that mess with the sigma sign in the middle, I tried to edit it but it was going to delete it.

I guess it will take a little practice writting with that stuff.

5. Nov 5, 2004

### Leo32

If in doubt of sums, just write out the first terms of the sum in full.
Sometimes you can see where the sum is heading in infinity...

Greetz,
Leo

6. Nov 5, 2004

### maverick280857

Well you know what you might be interested in this

$$\sum_{r = 0}^{n-1} \cos(\alpha + r\beta) = \cos(\alpha + \frac{n-1}{2}\beta) \frac{\sin(\frac{n\beta}{2})}{\sin(\frac{\beta}{2})}$$

and you can prove this too :-)

For your problem, you'd first note that the angles are in arithmetic progression and the above expression would be used with

$$\alpha = 0$$
$$\beta = \pi$$

Cheers
Vivek