Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Let \(\{a_n\}_{n=1}^{\infty}\) be a sequence of positive real number such that \(\sum_{n=1}^{\infty} a_n\) is divergent. Which of the following is true?
1
\(\sum_{n=1}^{\infty} \frac{a_n}{2-na_n} \) is convergent
2
\(\sum_{n=1}^{\infty} \frac{a_n}{2-n^2a_n} \) is convergent
3
\(\sum_{n=1}^{\infty} \frac{a_n}{1-a_n} \) is convergent
4
(i) and (iii) are true