Could someone give me a hand on this problem? I want to show that the set $\displaystyle K=\{x=(x_n): \sum x_n=1\}$ in complete in $\displaystyle C^n$

I tried to show that any convergent sequence in $\displaystyle K$ must have its limit in $\displaystyle C^n$ which means $\displaystyle K$ is closed in a complete space, but I failed to do this.