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Article: A sum concerning sequences.(Brief article)
- Article from:
- Smarandache Notions Journal
- Article date:
- January 1, 2001
- Author:
CopyrightCOPYRIGHT 2001 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract. Let A=[{a(n)}.sup.[infinity].sup.n=1] be a sequence of positive integers. In this paper we prove that if the trailing digit of a(n) is not zero for any n, then sum of a(n)/Rev (a(n)) is divergent.
Key words decimal number, reverse, sequence of positive integeers.
Let a=[a.sup.m] ... [a.sup.2][a.sup.1] be a decimal number. Then the deaimal number [a.sup.1][a.sup.2] ... [a.sup.m] is called the reverse of a and denote by Rev(a). For example, if a=123, then Rev(a)=321. Let S = [{s(n)}.sup.[infinity].sub.n=1] be a certain Smarandache sequence such that s(n)>0 for any positive integer n. In [1], Russo that proposed to study the limit
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