A sharp double inequality for sums of powers revisited

The proof of the monotonicity of the sequence n ↦ n Δ ( n ) , presented in the 2011 article “A Sharp double inequality for sums of powers” by V. Lampret, is corrected. Namely, it is demonstrated that, for S ( n ) : = ∑ k = 1 n ( k n ) n = ∑ j = 0 n ( 1 − j n ) n , the sequence n ↦ n ( e e − 1 − S (...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 14 - 11
Main Author Lampret, Vito
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 06.02.2025
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Applications of Mathematics
Estimate
Euler’s number
Graphs
Inequality
Limit
Mathematics
Mathematics and Statistics
Monotone sequence
Rate of convergence
Estimate
Euler’s number
Monotone sequence
Sums of powers
40A05
Limit
40A25
Rate of convergence
Inequality
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Summary:The proof of the monotonicity of the sequence n ↦ n Δ ( n ) , presented in the 2011 article “A Sharp double inequality for sums of powers” by V. Lampret, is corrected. Namely, it is demonstrated that, for S ( n ) : = ∑ k = 1 n ( k n ) n = ∑ j = 0 n ( 1 − j n ) n , the sequence n ↦ n ( e e − 1 − S ( n ) ) is strictly increasing.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-025-03253-2