A continuous, nowhere differentiable function: the Blancmange function

Let h(x) be the sawtooth function equal to |x| on [-1,1] and repeated periodically elsewhere.

Let hn(x)=h(2nx)/2n.

Then g(x)=h0(x)+h1(x)+h2(x)+... is a continuous and nowhere differentiable.

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Created by Dave Richeson using GeoGebra.