Bài giải:
a)
$25\leq x \leq 1000$
=>$x=${$25;26;27;...;998;999;1000$}
$S=25+26+27+...+998+999+1000$
Ta có:
$S=\frac{1000.(1000+1)}{2}-\frac{24.(24+1)}{2}=500200$
b)
$-37 \geq x \geq -1200$
=>$x=${$-37;-38;-39;...;-1198;-1199;-1200$}
$S=-37-38-39-...-1198-1199-1200$
Ta có:
$S=-\frac{1200.(1200+1)}{2}+\frac{36.(36+1)}{2}=-719934$