Math Help - Summation Problem

1. Summation Problem

Hi all,
I have a homework assignment from my calc. 2 class and one of the problems is really difficult for me. I am supposed to come up with a general formula for the summation from k = m to n of [(-1)^k^2][x^2k].
I don't want the answer, but I don't know where to begin.
I'm pretty sure I have to manipulate it into a simple geometric sum with only k as an exponent, but the algebra is working up my nerves.

Thanks in advance for the help

2. Also, is there a general rule or method for handling summations involving multiplication?

3. Originally Posted by swashbucklord
Hi all,
I have a homework assignment from my calc. 2 class and one of the problems is really difficult for me. I am supposed to come up with a general formula for the summation from k = m to n of [(-1)^k^2][x^2k].
I don't want the answer, but I don't know where to begin.
I'm pretty sure I have to manipulate it into a simple geometric sum with only k as an exponent, but the algebra is working up my nerves.

Thanks in advance for the help
Here is a hint

$a^{2k}=(a^2)^k$

and $(-1)^{k^2}=1$ for k even

$(-1)^{k^2}=-1$ for k odd

I hope this helps

4. thanks a lot, I ended up with

((-x^2) - (-x^2)^(n + 1))/(1 - (-x^2)) - ((-x^2) - (-x^2)^(m - 1))/(
1 - (-x^2))

I hope thats right

P.S. what program or application do you need to be able to write in mathematical equations or symbols?

5. I just realized a much simpler method and got the answer

((-x^2)^m - (-x^2)^(n + 1))/(1 - (-x^2))

which is equivalent to my previous answer

thanks again