Question

Let (an) be a sequence of real numbers defined by
$a_n=\begin{cases} 1 & \text{if } n \text{ is prime}\\\ -1 & \text{if } n \text{ is not prime} \end{cases}$
Let $b_n=\frac{a_n}{n}$ for n ∈ $\N$. Then

• A. both (an) and (bn) are convergent
• B. (an) is convergent but (bn) is NOT convergent
• C. (an) is NOT convergent but (bn) is convergent
• D. both (an) and (bn) are NOT convergent

Answer 1

Answer: (C)

(an) is NOT convergent but (bn) is convergent

Answer 2

The correct option is (C) : (an) is NOT convergent but (bn) is convergent.