 The partial sum formula_20 has only one digit accuracy, while six-figure accuracy requires summing about 400,000 terms.In the table below, the partial sums formula_3, the Shanks transformation formula_9 on them, as well as the repeated Shanks transformations formula_23 and formula_24 are given for formula_25 up to 12.The figure to the right shows the absolute error for the partial sums and Shanks transformation results, clearly showing the improved accuracy and convergence rate.