Problem is next:Let $E$ is normed vector space. If for every sequence $x_n$ that satisfies $\sum_{n=1}^\infty ||x_n|| < \infty$ exists $y \in E$ such that $\lim_{n\to \infty} \sum_{k=1}^n x_k = y$, then $E$ is complete.
We suppose that $x_n$ is Cauchy sequence and then we need to show that this sequence is convergent. I tried using definition of Cauchy sequence, but I can't get so much.
