UP TGT Mathematics Real Analysis Test Series - Part 2
The sequence a_n = 1 + 1/2! + 1/3! + ... + 1/n! is:
Type: MCQ • Marks: 1
The sequence a_n = 1 + 1/2! + 1/3! + ... + 1/n! is:
Options
A. Divergent to infinity
B. A Cauchy sequence converging to e - 1
C. Oscillating
D. Unbounded
Explanation
Correct Answer: Option 2 (A Cauchy sequence converging to e - 1). 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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