The sum of the first 40 terms of the series -1<sup>2</sup> + 2<sup>2</sup> - 3<sup>2</sup> + 4<sup>2</sup> - ... is:
Group the terms in pairs: \((-1^2 + 2^2) + (-3^2 + 4^2) + \dots + (-39^2 + 40^2)\)
Each pair is \((2k)^2 - (2k-1)^2 = 4k - 1\), for \(k = 1\) to \(20\).
Sum = \(\sum_{k=1}^{20}(4k - 1) = 4 \times \frac{20 \times 21}{2} - 20 = 840 - 20 = 820\)
Answer: (C) 820
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