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This article treats the summation of alternating infinite series, whose terms decrease to zero, and in addition satisfy certain 'convexity conditions'. Corrected partial sums are constructed, without any use of calculus, so as to accelerate the summation of the series. That is, the number of terms needed to achieve a desired accuracy, is significantly reduced. Examples and counter examples are given to demonstrate to the students the usefulness of the corrected summation.The introduction of these corrected sums well suits the teaching of infinite series, while emphasizing the difference between theoretical convergence and actual summation.

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Abstract. A version of Richtmyer's two step Lax-Wendroff scheme for solving hyperbolic systems in conservation form, is considered. This version uses only the nearest points, has second order accuracy at every time cycle and allows a time step which is larger by a factor of ]/d than Richtmyer's, where d is the number of spatial dimensions. The scheme appears to be competitive with the optimal stability schemes proposed by Strang and carried out by Gourlay and Morris.