Problem 1. Let (X, (, )) be an inner product space and let (yn) X be an orthonormal sequence. Let u EX and, for nEN define n Sn = (u, yj)yj. j=1 (1) Show, for all n, k EN with k>n, that (sn, Yk) = 0. (2) Show, for all n, k € N with k ≤ n, that (u — Sn, Yk) = 0. (3) Show, for all n E N and all v E span{y₁,..., yn}, that (u - sn, v) = 0.