In this paper we derive some identities of harmonic number sums with binomial coefficients, we also give integral representations for the sums. We recover some existing identities and introduce a number of new ones.\ud \u

In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by notations used in the body of the paper. After discussing some alternating Euler sums, we investigate the connection of integrals of inverse trigonometric and hyperbolic type functions to generate many new Euler sum identities. We also give some new identities for Catalan’s constant, Apery’s constant and a fast converging identity for the famous $\zeta \left(2\right)$ constant.

We establish integral identities for sums involving binomial coefficients and Harmonic numbers. Using the identities we recapture some established closed form representations of binomial sums and announce some new results.

We evaluate Euler-like sums involving harmonic numbers using expansions for powers of logarithmic, $\arctan$ and $\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}$ functions.