Can you move the sigma sign inside a sum?

[Fert]

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

can I just move the sigma sign inside the brackets? like

Cos(pi Sigma K)

just wondering because I have this on an assignment problem and we didn't learn it in class and the textbook doesn't cover it either. If I can move it inside the answer is easy so I am just assuming that's 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

 

[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.)

 

[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 textbook desn't cover it and we didn't take it in class.

 

[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.

 

[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

 

[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