Fourier Series plot

I’m trying to plot partial sum of Fourier series. I’ve finally managed to make it work but there are several things I don’t understand

f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi], Mod[x, 2 Pi] >= Pi}}]
g = FourierSeries[f, x, 2]
Plot[{g, f}, {x, -10, 10}]

My questions are :

1. Why does it stop working when I directly put the value of g in Plot (only f is plotted) ?

   f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi],Mod[x, 2 Pi]>= Pi}}]
   Plot[{FourierSeries[f, x, 2], f}, {x, -10, 10}]
   

2. Why does it stop working when I define g like this (only f is plotted)?

   g[x_] := FourierSeries[f, x, 2]
   Plot[{g[x], f}, {x, -10, 10}]
   

3. I also tried to add a slider to set the number terms to add. It seems to work but it makes Mathematica freeze…

   f = Piecewise[{{Mod[x, Pi], Mod[x, 2 Pi] < Pi}, {Mod[-x, Pi],Mod[x, 2 Pi] >= Pi}}]
   Slider[Dynamic[n], {1, 10, 1}]
   Dynamic[g = FourierSeries[f, x, n]]
   Dynamic[Plot[{g, f}, {x, -10, 10}]]
   

Thanks 🙂 !