$$\color{rgb(127,0,127)}f_k(x)=\frac{1}{2^k}\left| 2^kx-\left[ 2^kx+\frac{1}{2} \right] \right|$$

$$\color{rgb(0,0,255)}f(x)=\sum_{n=0}^{10}f_n(x)$$

$$\color{rgb(0,127,0)}g(x)=\sum_{n=0}^{k}f_n(x)$$