card stacking problem

How far can a stack of n books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_n for n books (in terms of book lengths) is half the nth partial sum of the harmonic series. This is given explicitly by d_n = 1/2 sum_(k = 1)^n 1/k = 1/2 H_n, where H_n is a harmonic number.

harmonic number | harmonic series