1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/41.猜想其规律,用含有_数学解答

1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4
1.猜想其规律,用含有n的字母的等式表示,并证明（n为正数）
2.用1 的规律计算1/（x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)

人气：325 ℃　时间：2019-10-24 02:36:38

解答

1...1/n(n+1)=1/n-1/(n+1)证明:1/n-1/(n+1)=[(n+1)-n]/[n(n+1)]=1/n(n+1)2...1/（x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)=1/(x-3)-1/(x-2)-2/(x-1)(x-3)+1/(x-2)-1/(x-1)=1/(x-3)-2/(x-1)(x-3)-1/(x-1)=0