INFINITE SERIES - Elsevier.com
6 CHAPTER 1. INFINITE SERIES To free the integral test from the quite restrictive requirement that the interpo-lating function f(x) be positive and monotonic, we shall show that for any function f(x) with a continuous derivative, the inflnite series is exactly represented as a sum of two integrals: XN2 n=N1+1 f(n) = Z N 2 N1 f(x)dx+ Z N 2 N1 N1
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