Hi all,

I can't solve the following , can anyone help?

Let X = { $\displaystyle (x_{n})_{n=1}^{\infty} : \sum_{n=1}^{\infty} n^{-2}| x_{n}| < \infty $ } , and a norm on this space is defined by : || x || = $\displaystyle sup_{n > 0} |x_{n}| n^{-2} $ Show that the space (X , || .||) is not complete and find its completion. Obviously I need to find a complete and non-convergent sequence in this space , can anyone give an idea ? For the completion , I don't have an idea any hint is appreciated