Journal of Integer Sequences, Vol. 14 (2011), Article 11.6.1

On the Summation of Certain Iterated Series

Ovidiu Furdui
Campia Turzii
405100 Cluj

Tiberiu Trif
Department of Mathematics
Babeş-Bolyai University


The paper gives a unified treatment of the summation of certain iterated series of the form $ \sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{n+m},$ where $ (a_{n})_{n\in \mathbb{N}}$ is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single series.

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(Concerned with sequences A000110 A094638.)

Received February 10 2011; revised version received May 9 2011. Published in Journal of Integer Sequences, May 17 2011.

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