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Find the sum of the series 1^2-2^2+3^2-4...

Find the sum of the series `1^2-2^2+3^2-4^2+\ldots-{2008}^2+{2009}^2`

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Verified by Experts

The correct Answer is:
B
Let any line through the origin meets the given lines at P and Q as shown in figure.

Now, from the figure, triangles OAP and OCQ are similar.
Therefore,
`(OP)/(OQ) = (OA)/(OC) = (9//4)/(3) = (3)/(4)`
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