# Dilution of a series

From Encyclopedia of Mathematics

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: http://www.encyclopediaofmath.org/index.php?title=Dilution_of_a_series&oldid=18098

This article was adapted from an original article by I.I. Volkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article