Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Let \(\{a_n\}_{n=1}^{\infty}\) be a sequence of non negative real number. Which of the following statement is not true?
1
If \(\sum_{n=1}^{\infty} a_n < \infty \) then \(\sum_{n=1}^{\infty} a_n^5 < \infty \)
2
If \(\sum_{n=1}^{\infty} a_n^5 < \infty \) then \(\sum_{n=1}^{\infty} a_n < \infty \)
3
If \(\sum_{n=1}^{\infty} a_n^{\frac{3}{2}} < \infty \) then \(\sum_{n=1}^{\infty} \frac{ a_n}{n} < \infty \)
4
(i) & (iii) both are correct.