Summation for y(x)=Absolute value(sin(x)) -pi<x<pi

[jennyjones]

i want to use the Fourier method to fins an summation for
y(x)=Absolute value(sin(x)) -pi<x<pi

i know that cos(pi*n)=(-1)^n

and get why they use cos(pi*(n+1))= (-1)^(n+1)

but why is then cos(pi*(n-1)) also (-1)^(n+1)


(see attachment)

THANX!

 

[jedishrfu]

look at the two expressions:

(-1)^(n+1) ==> (-1)^n * (-1)

and

(-1)^(n-1) ==> (-1)^n*(1/(-1)) = (-1)^n * (-1)

so they are interchangeable.

 

[jennyjones]

Thank you!