HarmonicNumber

Returns the nth Harmonic number.

Syntax

• HarmonicNumber(n)

  • n is a non-negative integer

Description

HarmonicNumber(n) is the nth Harmonic number, that is,

HarmonicNumber(n) = ∑(1/k, k, 1, n).

Examples

∑(HarmonicNumber(n)/(n⋅2^n), n, 1, 100)

0.822467033424	(=π²/12)

γ ≔ 0.57721566490153286060651209008240243104215933593992;

compute(HarmonicNumber(10^n)/(γ + ln(10^n)), n, 0, 10)

1.7324547146
1.0170732284
1.00096319859
1.00006678939
1.00000510844
1.00000041356
1.00000003474
1.00000000299
1.00000000026
1.00000000002
1