Question

观察下列等式：1*1/2=1-1/2，2*2/3=2-2/3，3*3/4=3-3/4，……请你计算（1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8

打错了，是请你计算（1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x（10-10/11）/1

Answer 1

解：关键在于逆应用条件1*1/2=1-1/2，2*2/3=2-2/3，3*3/4=3-3/4，由题意得
（1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x（10-10/11）/1
=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x....x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(整理简化运算)
=(1x2x3x...x10)x(1/10x1/9x1/8x1/7x....x1/2x1/1)x(1/2x2/3x3/4x.....x8/9x9/10x10/11)
=1/11
给点分吧！

Answer 2

解：关键在于逆应用条件1*1/2=1-1/2，2*2/3=2-2/3，3*3/4=3-3/4，由题意得
（1-1/2)/10 x (2-2/3)/9 x (3-3/4)/8 x ……x（10-10/11）/1
=(1x1/2x1/10)x(2x2/3x1/9)x(3x3/4x1/8)x....x(8x8/9x1/3)x(9x9/10x1/2)x(10x10/11x1/1)(整理简化运算)
=(1x2x3x...x10)x(1/10x1/9x1/8x1/7x....x1/2x1/1)x(1/2x2/3x3/4x.....x8/9x9/10x10/11)
=1/11

Answer 3

1/60

追问

现在呢

Answer 4

算到一半晕了。。。

追问

……