mrcy0becklittler mrcy0becklittler

07-04-2017
Mathematics

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What is the sum of 1 2 3 ... 81??

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LammettHash LammettHash

07-04-2017

[tex]S=1+2+3+\cdots+79+80+81[/tex]
[tex]S=81+80+79+\cdots+3+2+1[/tex]

[tex]\implies 2S=(81+1)+(80+2)+\cdots+(2+80)+(1+81)[/tex]
[tex]\implies 2S=81(82)[/tex]
[tex]\implies S=81(41)=3321[/tex]

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