How large must $N$ be in order for $$S_{N} = \sum_{k=1}^{N} \dfrac{1}{k}$$ to exceed 4? Note: Computer calculations show that for $S_{N}$ to exceed 20, $N = 272,400,600$ and for $S_{N}$ to exceed 100, $N \approx 1.5 \times 10^{43}$.

Answer: $N$ = .