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Sequences

Review question

Can we sum $1^2-2^2+3^2-4^2+\dotsb+ (2n-1)^2-(2n)^2$?
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Ref: R9819

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Suggestion

Hence, or otherwise, show that \[1^2-2^2+3^2-4^2+\dotsb+ (2n-1)^2-(2n)^2=-n(2n+1).\]

Could we group the terms in some way? This might help us to see a useful sequence.