Harmonic series sum approximation Question: $ 1 + 1/2 + 1/3+\dots+ 1/n &gt; 4.$
  Find the range of smallest value of n. 
  
  Answer: $n$ lies in $(20,60)$.
  
  Source: KVPY 2017.


To the best of my knowledge I find this series to be divergent and thus its sum can not be calculated. I couldn't think of a way to approximate value of $n$. Help is appreciated!
Yes, the sequence $H_n=1 + 1/2 + 1/3+\dots+ 1/n$ is strictly increasing and divergent. The question is asking for the minimal positive integer $n$ such that $H_n&gt;4$.

Hint. Note that for any $n\geq 2$,
$$\ln(n)=\int_{1}^n \frac{1}{x}dx  &lt;  H_n&lt;  1+\int_{1}^n \frac{1}{x}dx=1+\ln(n).$$
See for example Showing inequality for harmonic series.
You can approximate the harmonic series by using the fact that the nth partial sum of the harmonic series minus the natural logarithm of n approaches $\gamma$ as n approaches infinity