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.
Share and Cite:
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.
Cited by
No relevant information.