Rudin PMA p.154
Define $\phi$ as:
$\phi(x)=|x| ,\;\;\forall x\in [-1,1] \;\; \text{and}\;\; \phi(x+2)=\phi(x)$
Let $\delta_m=\frac{1}{2} 4^{-m}, \forall m\in\mathbb{Z}^+$ and fix $x\in\mathbb{R}$. Then, Rudin states that:
$|\sum_{n=0}^m (\frac{3}{4})^n \frac{\phi(4^n (x+\delta_m)) - \phi(4^n x)}{\delta_m}|≧ 3^m - \sum_{n=0}^{m-1} 3^n$
I don't understand why this inequality holds.
Please help me understand this..
Thank you in advance