Solve given equation to a approximate value

Question

Can some explain to me how the relation shown below gives $\log k$ on approximation?

$$x = \sum_{i=0}^{k-1} \frac{1 }{k-i}$$

Answer 1

Note that $$x = \sum_{i=0}^{k-1} \frac{1 }{k-i}= 1+1/2+1/3+...+1/k$$

Also note that the above sum is an approximation to $$ \int _1 ^k (1/x)dx = \ln k $$

That is reason behind the approximation.