Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Sequences & Series (Convergence)
Suppose (an)n ≥ 1 and (bn)n ≥ 1 are two bounded sequences of real numbers.
Which of the following is true?
1
limsupn→∞ (an + (-1)nbn) = limsupn→∞ an + |limsupn→∞ bn|
2
limsupn→∞ ((an + (-1)nbn) ≤ limsupn→∞ an + limsupn→∞ bn
3
limsupn→∞ (an + (-1)nbn) ≤ limsupn→∞ an + |limsupn→∞ bn| + |liminfn→∞ bn|
4
limsupn→∞ (an + (-1)nbn) may not exist
5
Question Not Attempted