Although the harmonic series does not converge, the partialsums grow very, very slowly
Chapter 9, Problem 96(choose chapter or problem)
Although the harmonic series does not converge, the partialsums grow very, very slowly. Take a right-hand sumapproximating the integral of f(x)=1/x on the interval[1, n], with x = 1, to show that12 +13 +14 + +1n < ln n.If a computer could add a million terms of the harmonicseries each second, estimate the sum after one year.
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