Question

观察下列等式：1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4，……

1.猜想并写出第n个等式.
2.请你计算:(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.....x(10-10/11)/1

Answer 1

1. nx(n/n+1)= n-(n/n+1)
2. 1x1/2=1-1/2,2x2/3=2-2/3,3x3/4=3-3/4，……
(1-1/2)/10x(2-2/3)/9x(3-3/4)/8x.....x(10-10/11)/1
=(1x1/2)/10x(2x2/3)/9x(3x3/4)/8x.....x(10x10/11)/1
=10/11

追问

=(1x1/2)/10x(2x2/3)/9x(3x3/4)/8x.....x(10x10/11)/1
............
=10/11
这两个中可不可以再完整一些

追答

=(1/2)/10x(4/3)/9x(9/4)/8x.....x(100/11)/1
=((1/2)x(1/10))x((4/3)x(1/9))x((9/4)x(1/8))x.....x(100/11) (注意约分）
=10/11