Notes on a general sequence
Abstract
Let {rn}n∈ℕ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and limits for the counting function of this sequence. All of the results are applied to some well-known sequences in mathematics.
Keywords
general sequence; asymptotic formulae; limit behavior; the number e
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Department of Statistics, Lorestan University, Iran Iran, Islamic Republic of
https://orcid.org/0000-0003-4027-9838
División Matemática, Universidad Nacional de Luján, República Argentina Argentina
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