Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Let (an) be a sequence of real numbers defined by
\(\rm a_n= \begin{cases}1 & \text { if } \rm n \text { is prime } \\ -1 & \text { if }\rm n \text { is not prime }\end{cases} \)
Let \(\rm b_n=\frac{a_n}{n}\) for n ∈ ℕ. Then
1
both (an) and (bn) are convergent
2
(an) is convergent but (bn) is NOT convergent
3
(an) is NOT convergent but (bn) is convergent
4
both (an) and (bn) are NOT convergent