MTH621 Midterm MCQs 2024 by Miss Mehwish

Past Papers for Mids./Finals are also Available · MTH621 (Mega File) · Mid Term (Live Quiz)

1. A sequence {sn} of real numbers is called a Cauchy sequence if for every ε > 0, there is an integer N such that |sn - sm| < ε if m, n ≥ N.

Correct option: >

2. The set of terms of {snk} is contained in the set of terms of {sn} implies

⬛ sup{sn} = sup{snk}. ⬜ {sn} is convergent. ⬜ sup{sn} < sup{snk}. ⬜ sup{sn} ≥ sup{snk}.

Correct option: sup{sn} = sup{snk}.

Q3. Which of the following sequences is NOT a Cauchy sequence?

⬛ {n}

Correct option: [−3, 3]

7. The limit of the sequence sn = (1/n) + (2(1 + 3/n) / (1 + 1/n)) is

⬜ 4 ⬜ 3 ⬛ 2 ⬜ 1

Correct option: 2

8. A divergent infinite series that does not diverge to ... is said to be oscillate.

⬜ ±1 ⬜ ±2 ⬜ None of these

Correct option: ±∞

9. If lim sup sn = ∞, then {sn}

⬜ is convergent. ⬜ {sn} has unique limit. ⬛ {sn} is not bounded above. ⬜ {sn} has limit inferior.

Correct option: {sn} is not bounded above.