Question

Consider the statements.
I. if \(s_{n} = \frac{1}{n}\), the sequence \(\{s_{n}\}\) is divergent.
II. if \(s_{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}\), the sequence \(\{s_{n}\}\) is convergent.
Which one of the following is correct?

• A. Both I and II are true
• B. I is true, but II is false
• C. I is false, but II is true
• D. Neither I nor II is true

Hint:

Do not confuse the convergence of a sequence $\{s_n\}$ with the convergence of a series $\sum s_n$.
The sequence $\{1/n\}$ converges to 0, but the harmonic series $\sum 1/n$ diverges to infinity.

Answer 1

The Correct Option is D