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Sum of the series $S = 1^{2} - 2^{2} + 3^{2} - 4^{2} + . . . - 2008^{2} + 2009^{2}$ is

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2019045

1005004

2000506

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Correct option is A

We can write S asS=(1−2)(1+2)+(3−4)(3+1)+…+(2007−2008) (2007+2008)+20092=−[1+2+3+4+…+2008]+20092=−12(2008)(2009)+20092=2019045

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Sum of the series S=12−22+32−42+...-20082+20092 is

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Sum of the series $S = 1^{2} - 2^{2} + 3^{2} - 4^{2} + . . . - 2008^{2} + 2009^{2}$ is