One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series
One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series作者机构：Department of Mathematics George Mason University Fairfax USA MCSP Department Roanoke College Salem USA
出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)
年 卷 期：2013年第3卷第3期
页 面：309-316页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Harmonic Series Biconvergence Non-Integer Series
摘 要：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.
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