# Math Help - Non differentiabilty

1. ## Non differentiabilty

consider summation[(1/2^n)h(3^nx)]
Consider summation[(1/3^n)h(2^nx)]
where h(x)=|x|
I'm trying to see whether these functions are continuous and differentiable.
I know summation[(1/2^n)h(2^nx)] is continuous and not differentiable, but am unsure about theseothers.

2. A little question: writing [for example...] 'h(2^nx)' do You mean $h(2^{n} x)$ or $h(2^{n x})$?...

Kind regards

$\chi$ $\sigma$

3. h(2^{n} x)

4. Very well!... one of the properties of $h(*)$ is that $h(a\ x)= |a|\ h(x)$ , so that...

$\displaystyle \sum_{n=0}^{\infty} \frac{h(2^{n}\ x)}{3^{n}} = h(x)\ \sum_{n=0}^{\infty} (\frac{2}{3})^{n} = 3\ h(x)$ (1)

Kind regards

$\chi$ $\sigma$