TITLE: Inclusion of $l^p$ space for sequences
QUESTION [16 upvotes]: Inclusion of $L^p$ spaces for functions has been discussed here. 
Does this apply to $l^p$ space of sequences similarly? 
I tried to show the following: For $1\leq p<q<\infty$, $l^q\subset l^p$ By using Hölder inequality but it doesn't seem to work.
My question is that is this true? If yes, what's the right way to prove it and what's a good counter example for showing $l^p\subset l^q$ is not true? Thanks.

REPLY [8 votes]: For completeness, a counterexample for $p>q$: pick $s\in (1/p,1/q)$ and consider the sequence $x_n=1/n^s$. This sequence is in $\ell^p$ but not in $\ell^q$.