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In this paper, we discuss a class of methods for summing sequences which are generalizations of a method due to Salzer. The methods are not regular, and in contrast to the classical regular methods, seem to work best on sequences which are monotone. In our main theorem, we determine a class of convergent sequences for which the methods yield sequences which converge to the same sum. where Ym is a simple closed curve encircling the integers 1,2, • • • , m, Re z > 0, z £ Tm, and (ß)k = p(p + 1) ■doi:10.1090/s0025-5718-1972-0303674-x fatcat:sh5lm5dkufetpjgbmh3xd7npwa