On the series of Kempner-Irwin type

Abstract

In 1914, Kempner proved that the series consisting of the inverses of natural numbers which are free of the digit 9 is convergent. In 1916, Irwin considered the convergence problem of the series containing the inverses of all numbers that contain a group of digits a number of times. These types of series are still under the attention of many mathematicians such as R. Baillie, T. Schmelzer, H. Behforooz, B. Farhi, etc. In this paper we will deal with the problem of computing the sum of series of Kempner-Irwin type.

2000 Mathematics Subject Classification. Primary 65B10; Secondary 11-04.

Key words and phrases. Kempner series, Irwin series, summation of slowly convergent series.