How to plot a complicated function in Sage Math

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I apologize in advance for my lack of knowledge and understanding of sage. In principle what I want to achieve is the visualization of this function:

$$g \mapsto \left|x - \lfloor{x}\rfloor - \frac{1}{2} \right|$$ $$f(x) := \sum_{j=0}^\infty 2^{-j}g(2^jx)$$

Though I am having trouble finding out how to do this. In the documentation I did not find any easy way to handle infinite series.

I am sure this would be very helpful to many that struggle with a math problem and need to see it to believe it. A conventional plotting program will not work here, hence I searched for a better tool and found Sage Math. Is it possible in sage? Do you have any TLDR material that I could look into?

Thank you for your help.