已知1-2/1=2/1,2/1-3/1=6/1,3/1-4/1=12/1,根据这些等式解答下列各题.（1）求值：1/1*2+1/2*3+1/3*4+1/4*5+1/5*6（2）化简：1/1*2+1/2*3+1/3*4+...+1/n(n+1)(3)若1/1*2+1/2*3+1/3*4+...+1/n(n+1)=19/20

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
=1-1/6
=5/6
1/1*2+1/2*3+1/3*4+...+1/n(n+1)
=1-1/2+1/2-1/3+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
1/1*2+1/2*3+1/3*4+...+1/n(n+1)=19/20=n/(n+1)
所以n=19

题目中你吧1除以2写成2除以1了吧，

高人呢

给的等式就是错误的！！！！

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6 =(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)=1-1/6=5/61/1*2+1/2*3+1/3*4+...+1/n(n+1)=(1-1/2)+(1/2-1/3)+……+[1/n-1/(n+1)]=1-1/(n+1)=n/(n+1)1/1*2+1/2*3+1/3*4+...+1/n(n...

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6=5/6
1/1*2+1/2*3+1/3*4+...+1/n(n+1)=n/(n+1)
1/1*2+1/2*3+1/3*4+...+1/n(n+1)=19/20
n=19