(1)2*[(1999-3)/4+1]=1000
-1+3=2,-5+7=2以此类推
(2)以前4个数为例
11+12-13-14=11-13+12-14=-4
100一共有25组这样的数
所以=-4*25=-100
(3)原式=(1990+1)*(2000-1)-1990*2000=1990*2000-1990+2000-1=9
(4)原式=472634²+472635²-(472634-1)×472635-472634×(472635+1)=472634²+472635²-472634×472635+472635-472634×472635-472634=472634²+472635²-2×472634×472635+1=(472634-472635)²+1=2
(5)以此为例1/1×3+1/3×5+1/5×7=1/1×(1+2)+1/3×(3+2)+1/5×(5+2)=1+2+1+2/3+1+2/5=3×1+2×(1+1/3+1/5)
(6)直接用等比数列公式
(7)直接用等差数列公式
(8)原式=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8=7/8