First, apologies for the notation.. the computer I am currently using does not support the various buttons to create proper notation. 1. The problem statement, all variables and given/known data Given h(x)=|x| over [-1,1], extend the definition such that h(x+2)=h(x). That is, make h(x) be a periodic sawtooth function. Now let hn(x)=(1/2n)h(2nx). Then define g(x)=sigma[hn(x)]=sigma[(1/2n)h(2nx)] as n goes from 0 to infinity. Define the sequence xm=1/2m, where m=0, 1, 2, ... Prove that [g(xm)-g(0)]/[xm-0]=m+1 and use this to prove that g'(0) does not exist. 2. Relevant equations 3. The attempt at a solution I really have no idea. The best I have been able to do is to write the function as: g(x)=sigma[(1/2n)|2nx|] as n goes from 0 to infinity and then substitute xm for x to yield: g(x)=sigma[(1/2n)|2n*(1/2m)|] as n goes from 0 to infinity and simplify it to: g(x)=sigma[(1/2)n|2n-m|] as n goes from 0 to infinity. Otherwise, I have no idea.