I need to prove by induction the following. The left hand side of the inequality is basically a harmonic serie where $H(1065^k)$. I've been able to complete this problem with $H(2^k)\ge 1 + \frac k2$, but can't seen to complete this problem...
$$\sum_{k=1}^{1065^k} \frac 1k \ge 1 + \frac {1064}{1065} k$$