proof writing - Proving inequality using induction

Question:

$ Prove\ for\ all\ natural\ n:\ \frac{1}{n+1}+\frac{1}{n+2}+\ldots +\ \frac{1}{3n+1}>1 $

I know that the base case holds. I.H: Assume it is true for $n = k$. Now I am not sure how to prove it for $n = k+1$.