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The sum of the products of the ten numbe...

The sum of the products of the ten numbers `+-1,+-2,+-3,+-4,+-5` taking two at a time is:

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Verified by Experts

We have,
`(1-1+2-2+..+5-5)^(2)`
`=1^(2)+1^(2)+2^(2)+2^(2)+…+5^(2)+5^(2)+2S`,
where S is the required sum. Hence,
`0=2(1^(2)+2^(2)+3^(2)+4^(2)+5^(2))+2S`
or S=-55
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