The generalization of Shanks' $e$-transformation to double series is discussed and a class of nonlinear transformations, the $\lbrack A/S \rbrack_R$ transformations ...

Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...