(10/9x7/8x6/13)÷(3/13x16/7x5/18)
=(6/9x10/8x7/13)÷(16/13x5/7x3/18)
=（2/3×5/4×7/13）÷(16/13×5/7×1/6)
=（5/3×2/4×7/13）÷(1/13×5/7×16/6)
=（5/3×1/2×7/13）÷(1/13×5/7×8/3)
=（5/3×1/2×7/13）÷(5/3×1/7×8/13)
=（1/2×7/13）÷（1/7×8/13）
=（7/2）÷（7/8）
=4
2/3x4x5+2/4x5x6+2/5x6x7+2/6x7x8+2/7x8x9+2/8x9x10=( )
=1/3*4-1/4*5+1/4*5-1/5*6+...+1/8*9-1/9*10
=1/3*4-1/9*10
=1/12-1/90
=13/180
俊狼猎英团队为您解答
①1/2X1/15+1/3X1/2
=1/2×1/3×(1/5+1)
=1/6×6/5
=1
②5/6X5/9+5/9X1/6
=1/6×5/9×(5+1)
=5/9
③3/9X7/16X2/9
=1/3×7/8×1/9
=7/216
④2/5X4X3/4
=2/5×3
=6/5
=1又1/5
⑤4/5X7/9X8/5
=224/225
⑥5/7X16X1/5
=1/7×16×1
=16/7
=2又4/7
3/(1×4)+3/(4×7)+3/(7×10)+3/(10×13)+3/(13×16)
=1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16
=1-1/16
=15/16
分析:1/1x3x5=1/4×(1/1*3 -1/3*5)
1/3x5x7=1/4×(1/3*5 -1/5*7)
1/5x7x9=1/4×(1/5*7 - 1/7*9)
1/7*9*11=1/4×(1/7*9 -1/9*11)
.....................
1/2003x2005x2007=1/4×(1/2003*2005 -1/2005*207)
所有的等式相加有
1/1x3x5+1/3x5x7+1/5x7x9+.....+1/2003x2005x2007
=1/4×(1/1*3 -1/3*5 +1/3*5 -1/5*7+....+1/2003*2005-1/2005*2007)
=1/4×(1/1*3 - 1/2005*2007)
=335336/4024035
结论:1/n(n+1)(n+2)=1/2×[1/n(n+1) - 1/(n+1)(n+2)]
1/n(n+2)(n+4)=1/4×[1/n(n+2) - 1/(n+2)(n+4)]
原式=3/7x5/13-3/7x3/13-(9/14-3/14)x(-11/13)
=6/91+3/7x11/13
=6/91+33/91
=39/91
=3/7
3/7X5/13-(9/14-3/14)X(-11/13)-3/7X3/13
=3/7X5/13+3/7X11/13-3/7X3/13
=3/7(5/13+11/13-3/13)
=3/7
3/10X49/9X16/91X130/21X15/4X8/9
=3/10X7^2/3^2X4^2/13*7X13*10/3*7X3*5/4X2*4/3^2
=160/21
巧算就是换一下分数的位置然后约分就行了
要不然越算越麻烦了
因为an=n*(n-1)/n+1 所以每个数可以看成2/3+（1+2/4）+（2+2/5）+（3+2/6）...+（8+2/11）=
1+2+3...+8+2/3+2/4+2/5...+2/11=36+2*（1/3+1/4+1/5+...1/11）
因为后面的那个是一个发散数列，好像没有求和公式，所以只能同分计算，当然可以把简单的算出来，剩下36+2*（1/4+1/5+1/8+1/10）+2*（1/3+1/6+1/7+1/9+1/11）这里就不继续了