Question

$\lim_{n \to \infty} \frac{1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{n}}{n}$ is

• A. 1
• B. 0
• C. 2
• D. 3

Hint:

Whenever you see a limit of the form $\frac{1}{n}\sum_{k=1}^n a_k$, immediately check $\lim_{n \to \infty} a_n$. If $a_n \to L$, then the average also converges to $L$ by Cauchy's First Limit Theorem!

Answer 1

The Correct Option is B