Acceleration of Series,
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The rate of convergence of infinite series can be accelerated by a suitable splitting of each term into two parts and then combining the second part of the n-th term with the first part of the n1-th term to get a new series and leaving the first part of the first term as an orphan. Repeating this process an infinite number of times, the series will often approach zero, and one obtains the series of orphans, which may converge faster than the original series. Heuristics for determining the splits are given.
- Theoretical Mathematics