We must test to see what happens when k is even and when k is odd. When k is eve

Question

We must test to see what happens when k is even and when k is odd.  When k is even cos(-?k) and cos(?k) = 1.  When k is odd cos(-?k) and cos(?k) =-1.

Test for odd: Replace cos(-?k) and cos(?k) with 1.

Test for odd: Replace cos(-?k) and cos(?k) with -1.

same problem as above!!!!

Did you get the same answer for both tests?  If so, then ak= the answer you got.

Did you get the opposite answers meaning the answers are the same but one is positive and one is negative?   If so, then ak=(-1^n) [answer you got]

Did you get a non-zero answer for the even test and zero for the odd test?  Then, replace k with 2k in the answer you got.  

Did you get a non-zero answer for the odd test and zero for the even test?  Then, replace k with 2k+1 in the answer you got.  

ak=

We must test to see what happens when k is even and when k is odd. When k is even cos(-?k) and cos(?k) = 1. When k is odd cos(-?k) and cos(?k) =-1.ak = 2 / pi k2 [ 1 - cos ( -pi k ) ] + 2 / pi k ) - 1 ] = [

Explanation / Answer

cos(-kPi)=cos(kPi) so what you put in the comment is :

ak = 4/(Pi*k)^2 * ( cos(Pi*k)-1) = 4/(Pi*k)^2 ( (-1)^k -1)

so a2k=0 and a(2k+1)=-8/(Pi(2k+1))^2

Sounds like Fourier coefficients to me :) right ?

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