Question Number 47413 by Tawa1 last updated on 09/Nov/18
$$\mathrm{Calculate}:\:\:\mathrm{1999}^{\mathrm{2}} \:−\:\mathrm{1998}^{\mathrm{2}} \:+\:\mathrm{1997}^{\mathrm{2}} \:−\:\mathrm{1996}^{\mathrm{2}} \:...\:−\:\mathrm{2}^{\mathrm{2}} \:+\:\mathrm{1}^{\mathrm{2}} \\ $$
Answered by mr W last updated on 09/Nov/18
$$=\left(\mathrm{1999}^{\mathrm{2}} \:−\:\mathrm{1998}^{\mathrm{2}} \right)\:+\:\left(\mathrm{1997}^{\mathrm{2}} \:−\:\mathrm{1996}^{\mathrm{2}} \right)+\:...+\left(\mathrm{3}^{\mathrm{2}} \:−\:\mathrm{2}^{\mathrm{2}} \right)\:+\:\mathrm{1}^{\mathrm{2}} \\ $$$$=\left(\mathrm{1999}\:+\:\mathrm{1998}\right)\:+\:\left(\mathrm{1997}\:+\:\mathrm{1996}\right)+\:...+\left(\mathrm{3}\:+\:\mathrm{2}\right)\:+\:\mathrm{1} \\ $$$$=\left(\mathrm{1999}+\mathrm{1}\right)×\mathrm{1999}/\mathrm{2} \\ $$$$=\mathrm{1000}×\mathrm{1999} \\ $$$$=\mathrm{1999000} \\ $$
Commented by Tawa1 last updated on 09/Nov/18
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$