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# help with sum

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Find the exact value of 2012-2002+1992-1982 +...+ 32 - 22 + 12 - 2

Mar 5, 2022

We can call two adjacent terms a pair. For example, 2012 and -2002 is a pair and 32, -22 is also a pair. And the sum of the two values in each pair is 10. There are 101 pairs in totally and the sum of all the pairs should be$$101\cdot10=1010.$$