Geometry of Figurate Numbers and Sums of Powers of Consecutive Natural Numbers

DOI10.1080/00029890.2020.1671129zbMath1454.11057OpenAlexW2994733743WikidataQ126539077 ScholiaQ126539077MaRDI QIDQ5207473

Semyon Litvinov, František Marko

Publication date: 2 January 2020

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2020.1671129

zbMATH Keywords

Bernoulli numbersfigurate numbersgeometric proof of Fermat's fundamental formulasums of powers of consecutive natural numbers

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Special sequences and polynomials (11B83) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (3)

Unnamed Item ⋮ Sums of Powers of Consecutive Integers and Pascal’s Triangle ⋮ A Note on the Geometry of Figurate Numbers

Cites Work

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• Linear algebra and the sums of powers of integers
• Proof Without Words: Sums of Triangular Numbers
• A Quick Route to Sums of Powers
• The Sum of the kth Powers of the First n Integers
• Sums of Powers of Natural Numbers by Coefficient Operation
• Sums of powers of integers: a little of the history
• Proof Without Words: Cotangent Double Angle Identity
• Proof Without Words: On Sums of Squares and Triangles
• Proof Without Words: Using Trapezoids to Compute Triangular Numbers
• Proof Without Words: Sums of Odd Integers
• Proof Without Words: Sum of Triangular Numbers

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