Irrationality of certain infinite series
نویسندگان
چکیده
In this paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! is presented. Furthermore, formulas for the base b digits are given which, however, are not computably effective. Finally we generalize our method and give a simple criterium for some fast converging series representing irrational numbers.
منابع مشابه
Irrationality of certain infinite series II
In a recent paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! and on the same lines a simple criterion for some fast converging series representing irrational numbers was given. In the present paper, we give some generalizations of our previous results. 1 Irrationality criterion Our considerations in [3] lead us to the following criterion for irrationality, where x...
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