Dilution of a series

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The inclusion of any finite number of zeros between adjacent terms of a series. For the series


a diluted series has the form

Dilution of a series does not affect convergence of the series, but it may violate summability of the series (after dilution a series (*) summable to the number by some summation method may turn out to be not summable at all by this method or may turn out to be summable to a number ).

How to Cite This Entry:
Dilution of a series. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article