# Thread: Maclaurin series for cos^2 (x) help

1. ## Maclaurin series for cos^2 (x) help

i understand that the number pattern is 1, -2, 8, -32, etc with values only in the even derivatives and 0.

However, the actual problem for me is to actually write the series. like i know it would look something like (-1)^n (??x^(2n))/(2n!)

The ?? I'm having a hard time with since that sequence of numbers (1, -2, 8...) i can't figure out. Thank you

2. Originally Posted by maximade
i understand that the number pattern is 1, -2, 8, -32, etc with values only in the even derivatives and 0.

However, the actual problem for me is to actually write the series. like i know it would look something like (-1)^n (??x^(2n))/(2n!)

The ?? I'm having a hard time with since that sequence of numbers (1, -2, 8...) i can't figure out. Thank you

$cos^2(x)=\frac{1}{2}+\frac{1}{2}cos(2x)$.

3. Yeah thats how i got my values 1,-2, 8, -32, etc. The problem is that I can't find the ?? of (-1)^n (??x^(2n))/(2n!), since that number sequence I can't really figure out