Recent content by jpe

Yeah, that was a good suggestion indeed, it seems almost trivial now. Let {x} be given by x_n=1/\sqrt{n} if n=m^2 for some m, 0 else. So we would have x={1,0,0,1/2,0,0,0,0,1/3,0, ...} for the first few terms. Then: \sum_{n=1}^\infty x_n^2 = \sum_{m=1}^\infty (1/\sqrt{m^2})^2=\sum...

Homework Statement Suppose we have a sequence {x} = {x_1, x_2, ...} and we know that \{x\}\in\ell^2, i.e. \sum^\infty x^2_n<\infty. Does it follow that there exists a K>0 such that x_n<K/n for all n? Homework Equations The converse is easy, \sum 1/n^2 = \pi^2/6, so there would be a finite...