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The following fractions are written in a row: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8,...

wishfulthinking's profile pic

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The following fractions are written in a row:

1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11

Prove that you can't insert the signs + and - between these numbers so that the result would be 0.

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shaznl1's profile pic

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The proving of it is actually really easy. Since the last fraction of this equation is a prime number 11 and adding other fractions to it would only result in a base with non-prime numbers( two integers timed together does not result a prime number). Therefore, there would be nothing in the first part of the equation that could cancel 1/11 out. This rule applies same for 1/3 1/5, 1/7 and 1/2. The fractions of the prime numbers at the bottom made it impossible. If these numbers were deleted, it is actually possible.

 

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