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Question Number 47413 by Tawa1 last updated on 09/Nov/18

$$\mathrm{Calculate}:{1999}^2-{1998}^2+{1997}^2-{1996}^2...-2^2+1^2$$

Answered by mr W last updated on 09/Nov/18

$$=({1999}^2-{1998}^2)+({1997}^2-{1996}^2)+...+(3^2-2^2)+1^2$$$$=(1999+1998)+(1997+1996)+...+(3+2)+1$$$$=(1999+1)\times 1999/2$$$$=1000\times 1999$$$$=1999000$$

Commented by Tawa1 last updated on 09/Nov/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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