有理数的巧算(1).-1+3-5+7-9+11-…-1997+1999(2).11+12-13-14+15+16-17-18+…+99+100(3).1991×1999-1990×2000(4).472634²+472635²-472633×472635-472634×472636(5).1/1×3+1/3×5+1/5×7+…+1/1997×1999 2000(6).1+1/3
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![有理数的巧算(1).-1+3-5+7-9+11-…-1997+1999(2).11+12-13-14+15+16-17-18+…+99+100(3).1991×1999-1990×2000(4).472634²+472635²-472633×472635-472634×472636(5).1/1×3+1/3×5+1/5×7+…+1/1997×1999 2000(6).1+1/3](/uploads/image/z/2703342-30-2.jpg?t=%E6%9C%89%E7%90%86%E6%95%B0%E7%9A%84%E5%B7%A7%E7%AE%97%EF%BC%881%EF%BC%89.-1%2B3-5%2B7-9%2B11-%E2%80%A6-1997%2B1999%EF%BC%882%EF%BC%89.11%2B12-13-14%2B15%2B16-17-18%2B%E2%80%A6%2B99%2B100%EF%BC%883%EF%BC%89.1991%C3%971999-1990%C3%972000%EF%BC%884%EF%BC%89.472634%26sup2%3B%2B472635%26sup2%3B-472633%C3%97472635-472634%C3%97472636%EF%BC%885%EF%BC%89.1%2F1%C3%973%2B1%2F3%C3%975%2B1%2F5%C3%977%2B%E2%80%A6%2B1%2F1997%C3%971999+2000%EF%BC%886%EF%BC%89.1%2B1%2F3)
有理数的巧算(1).-1+3-5+7-9+11-…-1997+1999(2).11+12-13-14+15+16-17-18+…+99+100(3).1991×1999-1990×2000(4).472634²+472635²-472633×472635-472634×472636(5).1/1×3+1/3×5+1/5×7+…+1/1997×1999 2000(6).1+1/3
有理数的巧算
(1).-1+3-5+7-9+11-…-1997+1999
(2).11+12-13-14+15+16-17-18+…+99+100
(3).1991×1999-1990×2000
(4).472634²+472635²-472633×472635-472634×472636
(5).1/1×3+1/3×5+1/5×7+…+1/1997×1999
2000
(6).1+1/3+1/3²+1/3³+…+1/3
★注:1/3 是三分之一三的两千次方
(7).1+4+7+…+244
(8).1 1/3-7/12+9/20-11/30+13/42-15/56
★注:1 1/3表示1又1/3
有理数的巧算(1).-1+3-5+7-9+11-…-1997+1999(2).11+12-13-14+15+16-17-18+…+99+100(3).1991×1999-1990×2000(4).472634²+472635²-472633×472635-472634×472636(5).1/1×3+1/3×5+1/5×7+…+1/1997×1999 2000(6).1+1/3
(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
额
楼上的,第二题没有25对。
只有22对,应该是(-4)*22+99+100=111