UP TGT Mathematics Real Analysis Test Series - Part 5
In the real number system R, a sequence is convergent if and only if it is:
Type: MCQ • Marks: 1
In the real number system R, a sequence is convergent if and only if it is:
Options
A. A Cauchy sequence
B. Oscillating
C. Unbounded
D. Monotonic only
Explanation
Correct Answer: Option 1 (A Cauchy sequence). Cauchy General Principle: In R, a sequence converges if and only if it is a Cauchy sequence (|a_n - a_m| < epsilon for n, m >= N). Every Cauchy sequence in R is bounded and convergent.
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