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Q)

Sum of series $1^2$-$2^2$+$3^2$-$4^2$+$5^2$+.....+$1001^2$ is

$(a)\;501501\qquad(b)\;1001001\qquad(c)\;1001\qquad(d)\;501500$

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A)
Answer : (a) 501501
Explanation : $S=1^2-2^2+3^2-4^2+\;.....\;+1001^2$
$S=(1-2)(1+2)\;+(3-4)(3+4)\;+........\;(1001)^2$
$S=\;-[1+2+3+-----\;1000]\;+(1001)^2$
$=\;-\frac{1}{2}*(1000)\;(1001)\;+(1001)^2$
$=501501.$
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