Combinatorial identities involving reciprocals of the binomial and central binomial coefficients and harmonic numbers

Abstract

We prove a general combinatorial formula involving the reciprocals of the binomial coefficients and the partial sum of an arbitrary sequence. Applying this formula we offer many combinatorial identities involving reciprocals of the binomial and central binomial coefficients and harmonic numbers; some of which have been considered previously and the others are new.

Keywords:

• Combinatorial identity
• binomial sum
• binomial coefficient
• central binomial coefficient
• harmonic number
• harmonic number sum

AMS CLASSIFICATIONS:

• Primary 05A10
• Secondary 05A19

Disclosure statement

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