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Chapter 1: Sums, Products and Discrete Fourier Transform
https://doi.org/10.1142/9789813275386_0001Cited by:0 (Source: Crossref)
Abstract:
Arithmetic series, geometric series and harmonic series play a central role in problems in theoretical and mathematical physics.
An arithmetic series is the sum of a sequence {sk}, k = 0, 1, … in which each term is calculated from the previous one by adding (or subtracting) a constant c. This means sk = sk−1 + c = sk−2 + 2c = … = s0 + c · k, where k = 1, 2, …. In particular one has (n ≥ 1)
s0+(s0+d)+(s0+2d)+⋯+(s0+(n−1)d)=12n(2s0+(n−1)d)
