Please HELP big maths comp

Sarah_G

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Sep 20, 2016
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Hey everyone.. Completely new to this site so don't judge!
So I'm doing a horrific competition at my school and I am stuck on this question, can anyone help?

Problem 11:
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 one cannot insert the signs + and — between these numbers so that the result would be 0


thanks, appreciate any help I can get!!
:confused:
 
A lot of times when doing a proof, it's actually beneficial to try and prove the opposite of what you're asked to prove, in order to set up a proof by contradiction. So, why not try that here? If you attempt to prove that you can get zero, then essentially you're trying to find two groups of fractions with equal sums. What happens if you try this? Remember that your goal is to prove this is impossible, because by doing so you will prove the assigned task as well.
 
Hey everyone.. Completely new to this site so don't judge!
So I'm doing a horrific competition at my school and I am stuck on this question, can anyone help?

Problem 11:
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 one cannot insert the signs + and — between these numbers so that the result would be 0


thanks, appreciate any help I can get!!
:confused:
If it helps, you can assume that the 1 has a plus sign [or minus sign, your preference] in front of it since, if it doesn't, just multiple the entire expression by -1 and the result would still be zero.

Oh, and if you prefer working with integers just multiply the given numbers by 27720 [the LCM of the denominators]
 
If it helps, you can assume that the 1 has a plus sign [or minus sign, your preference] in front of it since, if it doesn't, just multiple the entire expression by -1 and the result would still be zero.

Oh, and if you prefer working with integers just multiply the given numbers by 27720 [the LCM of the denominators]

Denis will love that......
 
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