Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Let \(\rm a_n=\frac{1+2^{-2}+\cdots+n^{-2}}{n}\) for n ∈ ℕ. Then
1
both the sequence (an) and the series \(\rm \displaystyle\sum_{n=1}^{\infty} a_n\) are convergent
2
the sequence (an) is convergent but the series \(\rm \displaystyle\sum_{n=1}^{\infty} a_n\) is NOT convergent
3
both the sequence (an) and the series \(\rm \displaystyle\sum_{n=1}^{\infty} a_n\) are NOT convergent
4
the sequence (an) is NOT convergent but the series \(\rm \displaystyle\sum_{n=1}^{\infty} a_n\) is convergent