Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Sequences and Series of Functions
Let \(\rm f(x)=\frac{\log (2+x)}{\sqrt{1+x}}\) for x ≥ 0, and \(\rm a_m=\frac{1}{m} \int_0^m f(t) d t\) for every positive integer m. Then the sequence \(\rm \left\{a_m\right\}_{m=1}^{\infty}\)
1
diverges to + ∞.
2
has more than one limit point.
3
Converges and satisfies \(\rm \displaystyle\lim _{n \rightarrow \infty} a_m=\frac{1}{2} \log 2 \)
4
Converges and satisfies \(\rm \displaystyle \lim _{n \rightarrow \infty} a_m=0\)