# Thread: substitution in a sum

1. ## substitution in a sum

I have problems with latex on the site, so i have enclosed a pdf file

now i have two sums and i have to do a substitution
m=n/2 if n is even and m=(n-1)/2 if n is odd
have can i substitute this in my sum?
so how can i go from the first sum to the second one with this substitution

thanks guys

2. Hello,
Originally Posted by kuntah
I have problems with latex on the site, so i have enclosed a pdf file

now i have two sums and i have to do a substitution
m=n/2 if n is even and m=(n-1)/2 if n is odd
have can i substitute this in my sum?
so how can i go from the first sum to the second one with this substitution

thanks guys
For the first one, you don't need to. Just use de Moivre's formula :
(cos(t)+i sin(t))^n=cos(nt)+sin(nt)
And then, it's the binomial expansion.

3. I have proven the first one
but I don't know how to get to the second one

So using the first sum I have to prove the second one
using a substitution
m=n/2 if n is even and m=(n-1)/2 if n is odd