Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
For n ∈ ℕ, let
\(a_n=\frac{1}{(3 n+2)(3 n+4)} \text { and } b_n=\frac{n^3+\cos \left(3^n\right)}{3^n+n^3} \text {. }\)
Then, which one of the following is TRUE?
1
\(\sum_{n=1}^{\infty} a_n\) is convergent but \(\sum_{n=1}^{\infty} b_n\) is divergent
2
\(\sum_{n=1}^{\infty} a_n\) is divergent but \(\sum_{n=1}^{\infty} b_n\) is convergent
3
Both \(\sum_{n=1}^{\infty} a_n\) and \(\sum_{n=1}^{\infty} b_n\) are divergent
4
Both \(\sum_{n=1}^{\infty} a_n\) and \(\sum_{n=1}^{\infty} b_n\) are convergent