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Introduction 1 0.1 Finite Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.11 Progressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.12 Sums of powers of natural numbers . . . . . . . . . . . . . . . . . . . . . . . . 1 0.13 Sums of reciprocals of natural numbers . . . . . . . . . . . . . . . . . . . . . . 3 0.14 Sums of products of reciprocals of natural numbers . . . . . . . . . . . . . . . 3 0.15 Sums of the binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Numerical Series and Infinite Products . . . . . . . . . . . . . . . . . . . . . . 6 0.21 The convergence of numerical series . . . . . . . . . . . . . . . . . . . . . . . 6 0.22 Convergence tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 0.23–0.24 Examples of numerical series . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0.25 Infinite products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.26 Examples of infinite products . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.3 Functional Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 0.30 Definitions and theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

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