Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Define the sequences \(\left\{a_n\right\}_{n=3}^{\infty}\) and \(\left\{b_n\right\}_{n=3}^{\infty}\) as
an = (log n + log log n)log n and bn = \(n^{\left(1+\frac{1}{\log n}\right)}\)
Which one of the following is TRUE?
1
\(\sum_{n=3}^{\infty} \frac{1}{a_n}\) is convergent but \(\sum_{n=3}^{\infty} \frac{1}{b_n}\) is divergent
2
\(\sum_{n=3}^{\infty} \frac{1}{a_n}\) is divergent but \(\sum_{n=3}^{\infty} \frac{1}{b_n}\) is convergent
3
Both \(\sum_{n=3}^{\infty} \frac{1}{a_n}\) and \(\sum_{n=3}^{\infty} \frac{1}{b_n}\) are divergent
4
Both \(\sum_{n=3}^{\infty} \frac{1}{a_n}\) and \(\sum_{n=3}^{\infty} \frac{1}{b_n}\) are convergent