UP TGT Mathematics Real Analysis Test Series - Part 1
The limit of the sequence a_n = (n!)^(1/n) / n as n -> infinity is:
Type: MCQ • Marks: 1
The limit of the sequence a_n = (n!)^(1/n) / n as n -> infinity is:
Options
A. 1
B. 0
C. 1/e
D. e
Explanation
Correct Answer: Option 3 (1/e). A sequence is a function from N to R. The limit L satisfies |a_n - L| < epsilon for all n >= N. Standard limit theorems and algebraic rules apply.
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