Proving Subspace Relation: lp and lq Sequences

[hedipaldi]

Homework Statement

how to prove that the sequences space lp is subspace of lq for p smaller than q?

Homework Equations

The Attempt at a Solution

I try to imply holder inequality but meanwile unsuccesfully

 

[jbunniii]

Hint: if $0 < x < 1$ and $0 < p < q$, then $x^q < x^p$.

 

[hedipaldi]

Yes,so simple. thank you very much.