0,1

"In 1968 John W. Wrench Jr calculated the exact minimum number of terms needed for the series to sum past 100; that number is 15 092 688 622 113 788 323 693 563 264 538 101 449 859 497. Certainly, he did not add up the terms.

"Imagine a computer doing so and suppose that it takes it 10^-9 seconds to add each new term to the sum and that we set it adding and let it continue doing so indefinitely. The jpb will have heen completed in not less than 3.5 * 10^17 (American) billion years." Havil.

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 23.

Boas, R. P. and Wrench, J. W. "Partial Sums of the Harmonic Series." Amer. Math. Monthly 78, 864-870, 1971.

Eric Weisstein's World of Mathematics, Harmonic Number

H_n ~= Ln(n) + Euler's Gamma Constant (A001620) + 1/(2n).

f[n_] := Floor[Exp[n - EulerGamma] - 1/2] + 1; Table[ f[10^n], {n, 0, 2}]

Cf. A002387, A001620.

Sequence in context: A134656 A128122 A082178 this_sequence A083973 A094212 A070832

Adjacent sequences: A082909 A082910 A082911 this_sequence A082913 A082914 A082915

nonn,bref

Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2003