If $S = 1^{2} - 2^{2} + 3^{2} - 4^{2} . . . .$ upto $n$ terms and $n$ is even, then $S$ equals _____

\frac{n (n + 1)}{2}

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\frac{n (n - 1)}{2}

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\frac{- n (n + 1)}{2}

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\frac{- n (n - 1)}{2}

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Solution

The correct option is B $\frac{- n (n + 1)}{2}$
$s = 1^{2} - 2^{2} + 3^{2} - 4^{2} . . . . . . u p t o . . .^{'} n^{'}$ term
$= (1 - 2) (1 + 2) + (3 - 4) (3 + 4) + . . . . + (n - 1 - n) (n - 1 + n)$
$= - 1 (1 + 2 + 3 + 4 + . . . + n)$
$S = - \frac{n (n + 1)}{2}$

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