PG entrance exam CUET PG 2025 Mock Test Mathematical Science Analysis Sequences & Series (Convergence)
Consider the series \(\sum_{n=1}^{\infty} \frac{1}{n^{m}\left(1+\frac{1}{n^{p}}\right)}\) where m and p are real numbers. Under which of the following conditions does the above series converge?
1
m > 1.
2
0 < m < 1 and p > 1.
3
0 < m ≤ 1 and 0 ≤ p ≤ 1.
4
m = 1 and p > 1.