# LOOK HERE: Analysis

1. Dec 4, 2008

### BobSun

1. The problem statement, all variables and given/known data
Let X be a normed linear space. Prove that X is complete if and only if $$\sum^{\infty}_{n=1} x_{n}$$ converges in X for all sequences ($$x_{n}$$) that satisfy $$\sum^{\infty}_{n=1} \left\|x_{n}\right\|$$< $$\infty$$

2. Dec 5, 2008

### morphism

What have you tried? This is actually a familiar fact from calculus. Do you remember how in R a series converged if it converged absolutely? And do you remember how that was proved? Same proof works here.