Let $\displaystyle \Phi(x)=\frac{2}{\sqrt{\pi}}\sum_{k=0}^{\infty}(-1)^k\frac{x^{2k+1}}{k!(2k+1)}$, i.e $\Phi$ is the MacLaurin series of the function $\displaystyle \frac{2}{\sqrt{\pi}}\int\limits_{0}^{x}e^{-t^2}dt$. Why using partial sums of the series gives us a bad computation for $\Phi(20)$, when the operations are done in floating point arithmetic?

Thanks a lot for the help!