Dilution of a series
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 ).
Dilution of a series. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Dilution_of_a_series&oldid=18098