We present a new proof of Johnsonbaugh’s estimates for the error in an alternating series based on an idea of R. M. Young. We also use this same idea to prove the convergence of the Euler transform and a corresponding error ...

The aim of this paper is to extend and refine the Ramanujan–Lodge harmonic number expansion into negative powers of a triangular number. We construct a faster asymptotic series and some new sharp inequalities for the ...