Sums of consecutive reciprocals
( go to the article → https://www.johndcook.com/blog/2021/01/23/sums-of-consecutive-reciprocals/ )
The sum of the reciprocals of consecutive integers is never an integer. That is, for all positive integers m and n with n ≥ m, the sum is never an integer. This was proved by József Kürschák in 1908. This means that the harmonic numbers defined by are never integers. The harmonic series diverges, so […] The post Sums of consecutive reciprocals first appeared on John D. Cook.
Jan. 23, 2021, 2:56 p.m.