观察下列算式,并进行计算 1/3×5=1/2×（1/3-1/5）,1/5×7=1/2（1/5-1/7）.

题目

观察下列算式,并进行计算 1/3×5=1/2×（1/3-1/5）,1/5×7=1/2（1/5-1/7）.
（1）求1/19×21 + 1/21×23 + 1/23×25 +.+1/97×99的值
（2）求1-2+3-4+5-6+.+2008-2008的值

答案

再坏也要爱
(1)
1/19×21 + 1/21×23 + 1/23×25 +.+1/97×99
=1/2(1/19-1/21)+1/2(1/21-1/23)+1/2(1/23-1/25)+.+1/2(1/97-1/99)
=1/2(1/19-1/21+1/21-1/23+1/23-1/25+.+1/97-1/99)
=1/2(1/19-1/99)
=(1/2)×(80/1881)
=40/1881
(2)
1-2+3-4+5-6+.+2008-2009
=(1-2)+(3-4)+(5-6)+.(2008-2009)
=(-1)×1004
=-1004