數學簡算(過程必留)

2022-10-07 06:15:23 字數 1094 閱讀 1455

1樓:匿名使用者

1)1/1×6+1/6×11+1/11×16+1/16×21

=1/5(5/1×6+5/6×11+5/11×16+5/16×21)

=1/5×(1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)

=1/5×(1-1/21)

=1/5×20/21

=4/21

2)1/8+1/24+1/48+1/80+1/120

=1/4(1/2+1/6+1/12+1/20+1/50)

=1/4(1/1×2+1/2×3+1/3×4+1/4×5+1/5×6)

=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)

=1/4×(1-1/6)

=5/24

3)(1/2+1/3+……+1/2004)(1+1/2+....+1/2003)-(1+1/2+....1/2014)(1/2+1/3+....+1/2003)

設1/2+1/3+....+1/2003=a

則原代數式可化為

(a+1/2014)(1+a)-(1+a+1/2014)a

=a+a²+1/2014+a/2014-a-a²-a/2014

=1/2014

2樓:匿名使用者

(1)1/1×6=(1/5)×(1-1/6)1/6×11=(1/5)×(1/6-1/11)1/11×16=(1/5)×(1/11-1/16)1/16×21=(1/5)×(1/16-1/21)1/1×6+1/6×11+1/11×16+1/16×21=(1/5)×(1-1/6+1/6-1/11+1/11-1/16+1/16-1/21)=4/21

(2)1/8+1/24+1/48+1/80+1/120=1/4×(1/2+1/6+1/12+1/20+1/30)=1/4×(1/1*2+1/2*3+1/3*4+1/4*5+1/5*6)

=1/4×(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)

=1/4×(1-1/6)

=1/4×5/6

=5/24

3樓:time小青

第二小問是三分之一的等比數列

用遞等式計算,能簡算的要寫出簡算過程

1 2.5 6 2.5 4 5,2.5 6 4 5,2.5 10 5,25 5,5 2 35.6 2.8 4.4 7.2,35.6 4.4 2.8 7.2 40 10,30 3 0.25 3.2 12.5,0.25 4 0.8 12.5,0.25 4 0.8 12.5 1 10,10 4 7.5 1...

計算下面各題(能簡算的要簡算,並寫出簡算過程)6 64 0 22 9 78 3 24 19 75

du1 6.64 0.22 9.78 3.36 zhi6.64 3.36 dao 0.22 9.78 10 10 20 回 2 75.1 24.19 75.1 24.19 75.1 75.1 24.19 24.19 0 48.38 48.38 3 36900 2060 1910 60 36900 1...

用簡便方法計算下面各題要求寫出簡算過程

1 內23 4 1.375 7.25 65 8 容 2.75 7.25 1.375 6.625 10 8,2 2 8888 9 1.125 888 1.125 8 9 9 8 999 1,1000 3 2000 1999 0.83 199.9 1.7 2000 1999 0.83 1999 0.17...