Let $l^p(\mathbb{N})=\left\{ \{x_n\}_{n=1}^{\infty} : \|x\|_p=\left(\sum\limits_{n=1}^{\infty}|x_n|^p\right)^{1/p} < \infty \right\}$ with $1 \leq p < \infty$.
I would like some insight on how to show that this is a Banach space. I know that in order to be a Banach space that it must be complete. So I would have to show every Cauchy sequences converges.
I have to admit that I need some insight as to how to even start this.