Let C[0,2pi] be the inner product space of complex continuous functions on [0,2pi].

let {$\displaystyle v_k$:k=1,2,3,....} be an orthonormal sequence in C[0,2pi], given by $\displaystyle v_k(x)=sinkx/pi$.

Give an example of a function u such $\displaystyle u\neq\sum_{k=1}<u,v_k>v_k$ sum from k=1 to infinity.

thanks for any help.