
Equation Proofs
I am having a lot of difficulty figuring this one out. The goal is to show that equations 1, 2, and 3, give the final simplified equation 4. I have always been more of a calculus person, and have trouble with these types of algebra problems.
http://rapidshare.com/files/449301420/GetEQ4.png
So far I have tried multiplying both S and Sigma together and attempted to put ga into the equation, which didn't really get me anywhere. Any help is appreciated!

I would plug Equations 2 and 3 into 4 and show that you get Equation 1, for an appropriate choice of N. Then, since all your steps are reversible, you've shown that which you were asked to show.

I plugged both 2 and 3 into the last equation and it simplified to this:
http://rapidshare.com/files/449308643/GetEQ4part2.png
The exponents still look incorrect and I missing something?

Nothing incorrect yet. Remember the laws of exponents, and simplify your expression a bit.

I was able to simplify the exponents a lot, and it looks better:
http://rapidshare.com/files/449313639/GetEQ4part3.png
I am still stuck with the ga term on the bottom though

You should have
on the bottom.
You now must choose the value of that makes it all work the same as Equation # 1.

Correct, I just saw that I forgot to raise the bottom ga to the nb power, that makes so much more sense!


Would it happen to be N= , that way the ga term on the bottom would disappear completely leaving only the ga^nb on the top?

Not quite. You need to end up with on top. Right now, you have on top, and on the bottom. Use the laws of exponents. What must be?

N=

There you go. I'd say you're done now, essentially. Just run your computations in reverse, and you can show that Equations 13 give you Equation 4.