rjensen
The Problem states:
If cn are the Fourier coefficients for f using the orthonormal set {fn}∞n=1, show:
⟨∞∑n=1cnfn,f−∞∑n=1cnfn⟩=0.
I am assuming f equals ∑∞n=1fn not, ∑∞n=1cnfn since the right side of the inner product would immediately reduce to zero? My guess is that it isn't that simple.