Sums and Products

Arithmetic series, geometric series and the harmonic series play a role in problems in theoretical and mathematical physics. An arithmetic series is the sum of a sequence { s_k }, k = 0, 1, … in which each term is calculated from the previous one by adding (or subtracting) a constant c. This means

s_k = s_k−1 + c = s_k−2 + 2c = … = s₀ + c · k

where k = 1, 2, …. A geometric series is a series with a constant ratio between sucessive terms…