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If $a_1,a_2, \dots,a_n$ are positive real numbers, then

$$\frac{a_1}{a_2} + \frac{a_2}{a_3} + \cdots + \frac{a_{n-1}}{a_n}+\frac{a_n}{a_1}$$

is always

  1. $\geq n$
  2. $\leq n$
  3. $\leq n^{1/n}$
  4. none of the above.
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