Question

Let $a_n = 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n}$ and $b_n = \sum_{k=1}^{n} \frac{1}{k^2}$ for all $n \in \mathbb{N}$. Then

• A. $(a_n)$ is a Cauchy sequence but $(b_n)$ is NOT a Cauchy sequence
• B. $(a_n)$ is NOT a Cauchy sequence but $(b_n)$ is a Cauchy sequence
• C. both $(a_n)$ and $(b_n)$ are Cauchy sequences
• D. neither $(a_n)$ nor $(b_n)$ is a Cauchy sequence

Answer 1

Answer: (B)

$(a_n)$ is NOT a Cauchy sequence but $(b_n)$ is a Cauchy sequence

Answer 2

The correct option is (B): $(a_n)$ is NOT a Cauchy sequence but $(b_n)$ is a Cauchy sequence