Three versions of an inequality
Three versions of the inequality Σⁿ⁻¹ᵢ₌₁ 1/aᵢ(aᵢ₊₁+1) ≥ (n/(1+Πⁿᵢ₌₁aᵢ)) - (1/(aₙ(a₁+1))) are formulated and proved, where a₁,...,aₙ>0 are real numbers. An open problem is formulated.
| Published in: | Notes on Number Theory and Discrete Mathematics |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
"Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences
2025-09-01
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| Subjects: | |
| Online Access: | https://nntdm.net/papers/nntdm-31/NNTDM-31-3-639-645.pdf |
| _version_ | 1848665430576594944 |
|---|---|
| author | Krassimir Atanassov |
| author_facet | Krassimir Atanassov |
| author_sort | Krassimir Atanassov |
| collection | DOAJ |
| container_title | Notes on Number Theory and Discrete Mathematics |
| description | Three versions of the inequality Σⁿ⁻¹ᵢ₌₁ 1/aᵢ(aᵢ₊₁+1) ≥ (n/(1+Πⁿᵢ₌₁aᵢ)) - (1/(aₙ(a₁+1))) are formulated and proved, where a₁,...,aₙ>0 are real numbers. An open problem is formulated. |
| format | Article |
| id | doaj-art-dfeb79bd2088499c8bd00a38ad281e44 |
| institution | Directory of Open Access Journals |
| issn | 1310-5132 2367-8275 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences |
| record_format | Article |
| spelling | doaj-art-dfeb79bd2088499c8bd00a38ad281e442025-10-30T07:17:17Zeng"Prof. Marin Drinov" Publishing House of Bulgarian Academy of SciencesNotes on Number Theory and Discrete Mathematics1310-51322367-82752025-09-0131363964510.7546/nntdm.2025.31.3.639-645Three versions of an inequalityKrassimir Atanassov0https://orcid.org/0000-0001-5625-071XInstitute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, BulgariaThree versions of the inequality Σⁿ⁻¹ᵢ₌₁ 1/aᵢ(aᵢ₊₁+1) ≥ (n/(1+Πⁿᵢ₌₁aᵢ)) - (1/(aₙ(a₁+1))) are formulated and proved, where a₁,...,aₙ>0 are real numbers. An open problem is formulated.https://nntdm.net/papers/nntdm-31/NNTDM-31-3-639-645.pdfarithmetic inequalitycombinatorics |
| spellingShingle | Krassimir Atanassov Three versions of an inequality arithmetic inequality combinatorics |
| title | Three versions of an inequality |
| title_full | Three versions of an inequality |
| title_fullStr | Three versions of an inequality |
| title_full_unstemmed | Three versions of an inequality |
| title_short | Three versions of an inequality |
| title_sort | three versions of an inequality |
| topic | arithmetic inequality combinatorics |
| url | https://nntdm.net/papers/nntdm-31/NNTDM-31-3-639-645.pdf |
| work_keys_str_mv | AT krassimiratanassov threeversionsofaninequality |