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Recently, Weniger (delta sequence) method has been proposed by the authors ofRef. [1] (Jentschura et al.) for resummation of truncated perturbation seriesin quantum field theories. Those authors presented numerical evidencesuggesting that this method works better than Pade approximants when we resum afunction with singularities in the Borel plane but not on the positive axis. Wepresent here numerical evidence suggesting that in such cases the combinedmethod of Borel-Pade works better than its analog Borel-Weniger, and that itmay work better or comparably well in some of the cases when there aresingularities on the positive axis in the Borel plane.Comment: 11 pages, 9 eps-figures, revtex; one reference added, one sentence  (in 3rd paragraph after Eq.(11)) added for better clarity, references update

BOREL–PADÉ VS BOREL–WENIGER METHOD: A QED AND A QCD EXAMPLE