Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Consider a sequence
{an}, an = (-1)n \(\left(\frac{1}{2}-\frac{1}{n}\right)\). Let
bn = \(\sum_{k=1}^n\) ak ∀ n ∈ ℕ
Then which of the following is true?
1
\(\lim _{n \rightarrow \infty}\)bn = 0
2
\(\limsup _{n \rightarrow \infty}\) bn > 1/2
3
\(\liminf _{n \rightarrow \infty}\) bn < -1/2
4
0 ≤ \(\liminf _{n \rightarrow \infty}\) bn ≤ \(\liminf _{n \rightarrow \infty}\) bn ≤ 1/2
5
Question Not Attempted