An infinite series [math]\sum_{n=1}^{\infty}z_n[/math] of complex numbers converges to the sum [math]S[/math] if the sequence [math]S_N=\sum_{n=1}^{N}z_n[/math] of partial sums converges to [math]S[/math]. We then write [math]\sum_{n=1}^{\infty}z_n=S[/math]. For example, [math]\sum_{n=1}^{\infty}z^n=\frac{1}{1-z}[/math].[br][br]Drag the point [math]z[/math] around to see what happens to the partial sums when [math]z[/math] is inside or out of the open ball [math]|z|=1[/math].