On the irrationality of factorial series II
نویسندگان
چکیده
In this paper we give irrationality results for numbers of the form ∑∞ n=1 an n! where the numbers an behave like a geometric progression for a while. The method is elementary, not using differentiation or integration. In particular, we derive elementary proofs of the irrationality of π and em for Gaussian integers m 6= 0.
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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