ACCELERATING THE APPROXIMATION OF SERIES
Raymond J. Collins · PRIMUS · 1994
Most calculus texts extensively discuss tests for the convergence and divergence of series, but give very little attention to evaluating and approximating series. The fact that series converge at different rates is also inadequately treated in most calculus texts. This article focuses on how, in our elementary calculus sequence, we have used easily derivable corrected partial sums to speed up the process of approximating slowly converging series. Examples are given together with a summary of the positive benefits of including material of this type in an elementary calculus sequence.