Convergence Rates of Subseries. Issue 2 (7th February 2019)

• Record Type: Journal Article
• Authors: Leonetti, Paolo
• Is Part Of: American Mathematical Monthly. Volume 126:Issue 2(2019)
• Page Start: 163
• Page End: 167
• Publication Date: 2019-02-07
• Subjects: Primary 40A35; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2019.1537761
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: Let( x n ) be a positive real sequence decreasing to 0 such that the series∑ n x n is divergent andlim inf n x n + 1 / x n > 1 / 2 . We show that there exists a constantθ ∈ ( 0, 1 ) such that, for eachℓ > 0, there is a subsequence( x n k ) for which∑ k x n k = ℓ andx n k = O ( θ k ) .