Question

In l2 let M be th set of all sequences x=(x1,...,xn,0,0,...) which have only a finite number of nonzero terms. Prove that Mis linear subspace of l2 which is not closed. As a hint consider the sequence x1=(1,0,0,...) x2=(1,1/2,0,0,...) x3=(1,1/2,1/4,0,0,...) , ... in M.