Visualizing an alternating sequence and its partial sums

\textrm{Specify your function } f, \textrm{ so that it produces an alternating series, with terms}\\ a_j = f(j). \textrm{ Red points are terms } a_j, \textrm{ while blue points are terms in the sequence } s_j \\ \textrm{of partial sums. The horizontal blue line approximates the limit/sum of the series.}