PG entrance exam IIT JAM 2025 Mock Test Mathematical Science Analysis Sequences & Series (Convergence)
Which of the following statements is TRUE?
1
\(\sum_{n=1}^{\infty} n^2 \log \left(1+\frac{1}{n^3}\right)\) is convergent
2
\(\sum_{n=1}^{\infty}\left(1-\cos \left(\frac{1}{n}\right)\right) \log n\) is convergent
3
\(\sum_{n=1}^{\infty} n^2 \log \left(1+\frac{1}{n^4}\right)\) is divergent
4
\(\sum_{n=1}^{\infty}\left(1-\cos \left(\frac{1}{\sqrt{n}}\right)\right) \log n\) is convergent