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UP TGT Mathematics Real Analysis Test Series - Part 5

If (a_n) is monotonically decreasing, then its supremum is equal to:

Type: MCQ • Marks: 1
If (a_n) is monotonically decreasing, then its supremum is equal to:
Options
A. Infinity
B. a_1 (First term)
C. Lim(a_n)
D. Infimum
Explanation
Correct Answer: Option 2 (a_1 (First term)). Monotone Convergence Theorem states that every monotonic bounded sequence converges. Increasing bounded above -> Supremum; Decreasing bounded below -> Infimum.
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