Abstract:
The class of sequences and series in which the Aitken process accelerates the convergence is considerably extended. It is proved that a proper subsequence of a slowly convergent sequence satisfies the sufficient condition for accelerating the convergence of the Aitken transformation. Two numerical examples illustrate the highly accurate limit extrapolation.
Key words:convergent sequences, series with positive terms, limit extrapolation, acceleration of series convergence, Aitken transformation, d'Alembert's ratio test, Raabe's test, iterations, high precision computations.
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