# Plotting partial sums of Fourier sine series

How do I plot this on Mathematica version 5.2?

$\frac{4}{\pi} \sin{x} + \frac{4}{3 \pi} \sin{3 x} + \cdots + \frac{4}{(2 N+1) \pi} \sin{(2 N+1) x}$

over $x \in [-\pi,\pi]$ for $N= 3, 6, 12, 24$.

I tried and got this error:

f[x_, n_] := (4/Pi) Sum[Sin[(2 k + 1) x]/(2 k + 1), {k, 0, n}];