An alternating sum of squares

EasyBrainteasers~3m

Evaluate $100^2 - 99^2 + 98^2 - 97^2 + \dots + 2^2 - 1^2$ .

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Pair terms: $100^2-99^2$ , $98^2-97^2$ , … and factor each as $(a-b)(a+b)$ .
Each pair is $a+b$ , so the total is $1+2+\dots+100$ .

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