>    # FOURIER COSINE SERIES OF A TRIANGLE WAVE

>   

>    # f(x) = |x|  on (-Pi,Pi); f is periodic with period 2*Pi.

>   

>    aodd := k -> 1/(2*k + 1)^2;

aodd := {k}  -> 1/((2*k+1)^2)

>    partialsum := K -> (Pi/2) - (4/Pi)*sum(aodd(k)*cos((2*k+1)*x), k=0..K);

partialsum := {K}  -> 1/2*Pi-4/Pi*sum(aodd(k)*cos((2*k+1)*x),k = 0 .. K)

>    plot(partialsum(0), x=-8..8);

[Maple Plot]

>    partialsum(0);

1/2*Pi-4/Pi*cos(x)

>    plot(partialsum(1), x=-8..8);

[Maple Plot]

>    plot(partialsum(5), x=-8..8);

[Maple Plot]

>    plot(partialsum(20), x=-8..8);

[Maple Plot]

>