what is the formula to calculate the irreducible fraction series as sum?

Question

I have a series like

sum = 1 + 1/2 + 1/3 + ... ... ... + 1/n

Suppose I know the value of n. so what is the formula to calculate sum?

Answer 1

This is no 'nice' closed formula for this. It's known that $$ \sum_{r=1}^n \frac1n \approx \log n \quad \text{(in some sense)}.$$ Have a Google search for 'harmonic series' to find out more information -- other search engines are available! In particular, I'd recommend looking at the Wikipedia article, and specifically this section of it. Hopefully this helps you! :)