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UP TGT Mathematics Real Analysis Test Series - Part 5

The sequence a_n = n / (2^n) is monotonically decreasing for all:

Type: MCQ • Marks: 1
The sequence a_n = n / (2^n) is monotonically decreasing for all:
Options
A. n >= 10
B. No n
C. n >= 1
D. n >= 2
Explanation
Correct Answer: Option 3 (n >= 1). Monotone Convergence Theorem states that every monotonic bounded sequence converges. Increasing bounded above -> Supremum; Decreasing bounded below -> Infimum.
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