APM  Vol.3 No.3 , May 2013
One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series
ABSTRACT

We examine variations of the harmonic series by grouping terms into “washings” that alternate sign with the number of terms in a washing growing exponentially with respect to a fixed base. The bases x = 1 and x = ∞ correspond to the alternating harmonic series and the usual harmonic series; we first consider other positive integral bases and further we consider positive real number bases with a unique way to make sense of adding a non-integral number of terms together. In both cases, we prove a remarkable result regarding the difference between the upper and lower convergent values of the series, and give some analysis of this behavior.


Cite this paper
C. Davis and D. Taylor, "One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 309-316. doi: 10.4236/apm.2013.33044.
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