A family of summation formulae involving harmonic numbers

Abstract

In terms of the derivative operator and a binomial sum from the telescoping method, we establish a family of summation formulae involving harmonic numbers. Meanwhile, a general recurrence relation is also deduced in accordance with Abel's lemma on summation by parts.

Keywords:

• telescoping method
• derivative operator
• harmonic numbers

2000 Mathematics Subject Classification:

• Primary: 05A19
• Secondary: 40A25

Acknowledgements

The authors are grateful to the reviewer for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Funding

The work is supported by the Natural Science Foundations of China [grant numbers 11301120, 11201241];Jiangsu Qing Lan Project QL2014.