The sequence is defined for positive integers . Which of the following statements is true?

Answer and explanation

Correct answer: A. The least value of is

  1. Step 1: , with equality at , so the least value is .
  2. Step 2: The others fail: and ; shows it is not increasing everywhere; only for among positive integers; so it is increasing after .
Answer
The least value of is .
Why not the others: The sequence decreases up to and increases afterwards, so it has one least value but is neither always increasing nor eventually decreasing.

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