Prove that if n > 1, the partial sum of the harmonic series is not an integer.

Let 2^K be the largest power of 2 that is less than or equal to n and let M be the product of all odd integers that are less than or equal to n. Suppose that s_n = m, an integer. Then M2^K_Sn = M2^Km. The right side of this equation is even. Prove that the left side is odd by showing that each of its terms is an even integer, except for the last one.