UP TGT Mathematics Real Analysis Test Series - Part 1
The sequence a_n = sin(n * pi / 2) is:
Type: MCQ • Marks: 1
The sequence a_n = sin(n * pi / 2) is:
Options
A. Divergent to infinity
B. Bounded and convergent
C. Oscillates finitely between -1, 0, 1
D. Convergent to 1
Explanation
Correct Answer: Option 3 (Oscillates finitely between -1, 0, 1). A sequence converges if it approaches a unique finite limit L. Otherwise, it diverges (tends to infinity or oscillates). Every subsequence of a convergent sequence converges to the same limit.
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