The harmonic series Hn = n j=1(1/j ) is known to diverge, but on a computer it will appear to converge. Compute Hn until the value no longer changes with n. Compare the stopping point with what can be...

The harmonic series Hn = n j=1(1/j ) is known to diverge, but on a computer it will appear to converge. Compute Hn until the value no longer changes with n. Compare the stopping point with what can be guessed analytically, using εm and the approximation

             Hn = 1 + 1/2 + 1/3 +···+ 1/n = .577215664 + log n + o(n)

by equating εm and (n + 1)−1 /Hn (see Knuth 1997a, p. 160).