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The Euler transformation can accelerate the convergence of an alternating infinite series by computing averages of each pair of successive partial sums in the sequence. This is equivalent to joining up the midpoints of the lines between each value when the partial sums of the sequence are plotted.
Contributed by: Eliot Ball (April 2012)
Open content licensed under CC BY-NC-SA
Wolfram Demonstrations Project
Published: April 16 2012