Nicole Oresme (1323 - 1382 A.D.)

Among the many contributions of Nicole Oresme, Bishop of Lisieux in Normandy were the laws of exponents xm xn = xm+n and his proof that the harmonic series
H = 1 + 1/2 + 1/3 + 1/4 + ...
diverges. The idea is to arrange the sum in ever larger groups: a group of one term, then two, then four, etc. Try to complete Oresme's proof with this hint and the advantage of the 600 years separating us from him.

Reference: Boyer p 263-267.