UP TGT Mathematics Real Analysis Test Series - Part 2
If (a_n) and (b_n) are Cauchy sequences, then (a_n + b_n) is:
Type: MCQ • Marks: 1
If (a_n) and (b_n) are Cauchy sequences, then (a_n + b_n) is:
Options
A. Not a Cauchy sequence
B. Unbounded
C. A Cauchy sequence
D. Divergent to infinity
Explanation
Correct Answer: Option 3 (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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