Fourier wave saw tooth

Fourier wave saw tooth

N = 8 (slider from 1 to 50, step 1)
f = Sum(Sequence[(-1)^(n) * sin(n * x) / n, n, 1, N])
F(x) = -2 * f(x)
texte1: "F(x) = " + "2 \sum_{k=1 }^{k=" + N + "}  \frac{ sin(k x) }{k }  " + " = " + (LaTeX[F])