Suppose you're given the following Fourier coefficients for a function on the interval $[-\pi,\pi]$: $\displaystyle a_0 = -3$, $\displaystyle a_k = 0$ for $k \geq 1$, and $\displaystyle b_k = \frac{6 (-1)^{k}}{k}$ for $k \geq 1$. Find the following Fourier approximations to the Fourier series $\displaystyle a_0 + \sum_{n=1}^{\infty} (a_n\cos(nx) + b_n\sin(nx))$.

$F_0(x) =$

$F_1(x) =$

$F_2(x) =$

$F_3(x) =$