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Review question

Can we sum the first $2n$ terms of $1^2-3^2+5^2-7^2+\cdots$?
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Ref: R5416

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Question

By bracketing the terms in pairs, or otherwise, find the sum of \(2n\) terms of the series \[1^2-3^2+5^2-7^2+\cdots.\]

Hence show that the sum of \(2n+1\) terms is \(8n^2+8n+1\).