Question: Show that $\imath ^{p}$ is complete
On the space of sequence $\imath , for 1\leq p<\infty \left \| x \right \|_{p}:=\left ( \sum_{I=1}^{\infty} \left \| x_{i} \right \|^{p}\right )^{\frac{1}{p}}$
and $\imath ^{p}:=\left \{ x \in \imath : \left \| x \right \|_{p}<\infty \right \}$ is a normed space.
I think what I do need to show is that every Cauchy sequence function in $\imath ^{p}$ converges.
However, I am facing some issues getting the ball rolling.
Any hint is appreciated. Thanks in advance.