The goal is to show that $\sup{|u|} \leq C|\Omega|^{\frac{1}{n} - \frac{1}{p}}||Du||_p$ in the case $p>n$.
There is a point in the proof that I just am not getting. First, the notation:
Let $n' = \frac{n}{n-1}, p' = \frac{p}{p-1}, \delta = \frac{n'}{p'}$ It is shown in the proof that if $\tilde{u} = \frac{\sqrt{n}|u|}{||Du||_p}$ that
$||\tilde{u}||_{n'\delta^v} \leq \delta^{v\delta^{-v}}||\tilde{u}||_{n'\delta^{v-1}}^{1-\delta^{-v}} $
This part I'm ok with. Then the book makes the statement "Iterating from $v=1$ ,we get for any $v$"
$||\tilde{u}||_{\delta^v} \leq \delta^{\sum{v\delta^{-v}}}.$
I don't see how this follows. Could you maybe give some insight?