f(x) = x(π –x) on [0, π]

Find:

a)Odd completion (sine series)

f(x) ~ ∑bnsin(nx) where bn= 2/π 0∫π f(x)sin(nx)dx

b)Even completion (cosine series)

f(x) ~ a0/2 + ∑ancos(nx) where an= 2/π 0∫π f(x)cos(nx)dx anda0/2 = 1/π 0∫π f(x)dx

c) Use the above results to show ∑1/n^2 = π^2 /6

I get:

Odd completion = ∑(2/n^3)(1 – (-1)^n)sin(nx)

Even completion = (π ^2 /6)+ ∑(-2/n^2)(1+(-1)^n)cos(nx)

But I don’t know how to manipulate these to show that part c) is true