# Summation Problem

• May 29th 2009, 01:57 PM
swashbucklord
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
• May 29th 2009, 01:59 PM
swashbucklord
Also, is there a general rule or method for handling summations involving multiplication?
• May 29th 2009, 02:29 PM
TheEmptySet
Quote:

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

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

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

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

I hope this helps
• May 29th 2009, 03:14 PM
swashbucklord
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?
• May 29th 2009, 03:22 PM
swashbucklord
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