# Difference between revisions of "Dilution of a series"

$$\label{eq:1} \sum\limits_{k=0}^{\infty}u_k$$
$$u_0+0+\dots+0+u_1+0+\dots+0+u_2+\dots$$ Dilution of a series does not affect convergence of the series, but it may violate summability of the series (after dilution a series \eqref{eq:1} summable to the number $s$ 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 $a\ne s$).