Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps, including linear, quadratic, cubic, and higher-order forms. Using elementary techniques from differentiation and integration, the approach produces polynomial expressions that represent total sums, even when each term is raised to a positive integer power. As a result, Bernoulli numbers emerge naturally in the formulas, linking the approach to classical results in a concise and accessible manner.
Ahmed Abdalmuhsin Abdalsahib
数学
Ahmed Abdalmuhsin Abdalsahib.Deriving Closed-Form Expressions for Arithmetic Sequence Sums Raised to Integer Powers via Calculus[EB/OL].(2025-07-16)[2025-08-18].https://arxiv.org/abs/2507.13402.点此复制
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