# Math discrete: Proof by induction of harmonic serie

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...

$$\sum_{k=1}^{1065^k} \frac 1k \ge 1 + \frac {1064}{1065} k$$

• Having $k$ as a dummy variable and also as a part of the answer is bad practice. Better to write $$\sum_{r=1}^{1065^k}{1\over r}\ge1+{1064\over1065}k$$ – Gerry Myerson Nov 14 at 1:01
• Can you show $$\sum_{1065^{k-1}+1}^{1065^k}{1\over r}\ge{1064\over1065}$$ – Gerry Myerson Nov 14 at 1:03
• I actually wrote i=1 1/i I have no idea why I wrote k on both sides haha – Ian Peng Nov 14 at 1:03
• I can show $$\ge \frac{1}{1065}$$ but I don't know about $$\frac {1064}{1065}$$ – Ian Peng Nov 14 at 1:08
• How many terms are in the sum, and what's the smallest of those terms? – Gerry Myerson Nov 14 at 1:09