Why Isn't It Reducible?

Algebra Level 4

Let \[ A= \frac{1}{2} \times \frac{3}{4} \times \frac{5}{6} \times\cdots\times \frac{2013}{2014}\] \[ B= \frac{2}{3} \times \frac{4}{5} \times \frac{6}{7} \times\cdots \times \frac{2012}{2013}\] \[ C= \frac{1}{ \sqrt{2014} } \]

Which of the following statements is true?
\( 1. A < B < C \)
\( 2. A < C < B \)
\( 3. B < A < C \)
\( 4. B < C < A \)
\( 5. C < A < B \)
\( 6. C < B < A \)
\( 7. \) Two of them are equal
\( 8. \) All of them are equal

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