منابع مشابه
Euler and His Work on Infinite Series
Leonhard Euler is one of the greatest and most astounding icons in the history of science. His work, dating back to the early eighteenth century, is still with us, very much alive and generating intense interest. Like Shakespeare and Mozart, he has remained fresh and captivating because of his personality as well as his ideas and achievements in mathematics. The reasons for this phenomenon lie ...
متن کاملSome 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....
متن کاملOn Faster Convergent Infinite Series
Recommended by Laszlo Toth Suffcient conditions, necessary conditions for faster convergent infinite series, faster τ-convergent infinite series are studied. The faster convergence of infinite series of Kummer's type is proved. Copyright q 2008 Dušan Hoí y et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distributi...
متن کاملInfinite Series
so π is an “infinite sum” of fractions. Decimal expansions like this show that an infinite series is not a paradoxical idea, although it may not be clear how to deal with non-decimal infinite series like (1.1) at the moment. Infinite series provide two conceptual insights into the nature of the basic functions met in high school (rational functions, trigonometric and inverse trigonometric funct...
متن کاملNotes on Infinite Sequences and Series
We represent a generic sequence as a 1 , a 2 , a 3 ,. .. , and its n-th as a n. In order to define a sequence we must give enough information to find its n-th term. Two ways of doing this are: 1. With a formula. E.g.: a n = 1 n a n = 1 10 n a n = √ 3n − 7 2. With a recursive definition. 1.2. Limit of a Sequence. We say that a sequence a n converges to a limit L if the difference |a n − L| can b...
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 1991
ISSN: 0315-0860
DOI: 10.1016/0315-0860(91)90369-9