In this solutions manual on PDF page 836, the answer to Section 12.1 #7 calculates the Fourier coefficient a_n to be (1 - (-1)^n)/(n^2 π^2), thus the cosine term in the sum should be (1 - (-1)^n)/(n^2 π^2) cos(nπx). However, in the final solution it is written as 2/(π^2) * (cos(2n + 1)πx)/((2n + 1)^2). How is this transition made?