# Odd net forces in a circle = 0

#### RAz

I proved that all even vectors in a circle than pull outwards have a net force of 0. I'm having trouble with odd vectors.

What I've managed to do so far:

$$\displaystyle sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k) =sin\frac{2\pi}{n}-sin\frac{2\pi}{n}(k)=0$$

I'm having trouble with doing it for cos, plus I don't know if I'm solving it correctly. Thanks #### dwsmith

MHF Hall of Honor
$$\displaystyle sin\frac{2k\pi}{n}-sin\frac{2\pi}{n}(n+k)$$

Wrong factorization.

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#### RAz

Well kind of, that is the one I used. We can use any one necessary. We weren't given any equation, we were just asked to prove it.

I proved it for n=3 with real angles, and by adding the vectors it's net force is 0. I also did this for n>3 when n is even. It's when n>3 and odd that I'm having trouble with.

#### dwsmith

MHF Hall of Honor
Well kind of, that is the one I used. We can use any one necessary. We weren't given any equation, we were just asked to prove it.

I proved it for n=3 with real angles, and by adding the vectors it's net force is 0. I also did this for n>3 when n is even. It's when n>3 and odd that I'm having trouble with.
$$\displaystyle sin\left(\frac{2\pi}{n}(n+k)\right)$$

Is everything supposed to be part of sine function?

#### RAz

$$\displaystyle sin\left(\frac{2\pi}{n}(n+k)\right)$$

Is everything supposed to be part of sine function?
No it doesn't have to be, as when I was proving when N was even I broke it up.

The question was this: All vectors exert forced of the same magnitude F. Calculate the net force on all the vectors when N is any integer greater than 3.

So yeah, I've done if for N=3 and N>3 when N is even. We can do anything to make it work. Thanks for your help so far ;D

#### dwsmith

MHF Hall of Honor
No it doesn't have to be, as when I was proving when N was even I broke it up.

The question was this: All vectors exert forced of the same magnitude F. Calculate the net force on all the vectors when N is any integer greater than 3.

So yeah, I've done if for N=3 and N>3 when N is even. We can do anything to make it work. Thanks for your help so far ;D
Use math induction to prove it.
start by showing p(3)
assume p(k)
show p(k+1)