On multiplication of infinite series
نویسندگان
چکیده
منابع مشابه
Some Remarks on Infinite Series
In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....
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(1 .2) E(k)ak = Sn,j k=1 k = j (modn!) for n=1, 2,. .. and O~j-n!-1. When sn , j =0 for all n and j, (1 .1) follows automatically. Since every arithmetic progression with modulus m is a disjoint union of (m-1)! arithmetic progressions with modulus m!, Theorem 1 follows from Theorem 2. Also, by using this argument and (1 .2), we see that in Theorem 2 each series Z E (n) an is, n=b(mod m) in fact...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1948
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-10-1-104-112