On some special infinite series

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....

The Integrity of Some Infinite Series

On Some Infinite Series Related to the Twin Primes

It is shown that all positive integers can be divided into numbers that can lead to a pair of twin primes by a simple algebraic operation and numbers that cannot. The paper devises a formula for finding the numbers in each category, and shows that the numbers in the second category can be arranged in infinite groups and super-groups with an inner symmetry, a precise interval length and a well-d...

Characterization on Some Absolute Summability Factors of Infinite Series

A general theorem concerning some absolute summability factors of infinite series is proved. This theorem characterizes as well as generalizes our previous result [4]. Other results are also deduced.

On 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...