The summation

1/1 + 1/2 + 1/3 + 1/4 + ... + 1/n

is equal to the nth harmonic number, denoted H_{n}. The nth harmonic number obeys the inequalities

ln (n + 1) ≤ H

_{n}≤ (ln n) + 1

and therefore H_{n} = Θ(log n). The harmonic numbers often arise in the analysis of algorithms, with randomized quicksort being a particularly nice example.