Let [math]h(x)[/math] be the sawtooth function equal to [math]|x|[/math] on [math][-1,1][/math] and repeated periodically elsewhere.[br][br]Let [math]h_n(x)=h(2^nx)/2^n[/math].[br][br]Then [math]g(x)=h_0(x)+h_1(x)+h_2(x)+\cdots[/math] is a continuous and nowhere differentiable.