1.解:(1)|x_1-x_2|=|2-5|=3.
(2)|x_2-x_1|=|-5-2|=7.
(3)|x_2-x_1| = |-3-6|=9.
(4)|x_2-x_1| = |-6-(-3)|=3.
2.解:当n为偶数时,(〖(+1)〗^n+〖(-1)〗^n)/2=(1+1)/2=1;当n为奇数时,(〖(+1)〗^n+〖(-1)〗^n)/2=(1+(-1))/2=0.所以(〖(+1)〗^n+〖(-1)〗^n)/2的值为1或0.
(2)由(1)得原式=-50+101=51 .
(3)当n为偶数时,原式=(-1)×n/2=-n/2;当n为奇数时,原式=(-1)×(n-1)/2+n=(n+1)/2.