Let a_1, a_2, a_3, \ldots be a monotonically decreasing sequence of positive real numbers converging to zero. Suppose that \sum_{i=1}^{\infty} \frac{a_i}{i} diverges. Show that \sum_{i=1}^{\infty} a_i^{2^{2017}} also diverges. You may assume in your proof that \sum_{i=1}^{\infty} \frac{1}{i^p} converges for all real numbers p>1. (A sum \sum_{i=1}^{\infty} b_i of positive real numbers b_i diverges if for each real number N there is a positive integer k such that b_1+b_2+\cdots+b_k>N.)