观察: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.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)

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观察: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.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)

观察: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.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
观察:
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.观察规律,用含n(n为正整数)的等式表示出来,并证明
2.用1的规律计算:
1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)

观察: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.观察规律,用含n(n为正整数)的等式表示出来,并证明2.用1的规律计算:1/(x-2)(x-3) - 2/(x-1)(x-3) + 1/(x-1)(x-2)
1.1/n(n+1)=1/n-1/(n+1)
等式右边=1/n-1/(n+1)
通分=(n+1-n)/n(n+1)=等式左边
所以成立
2.原式=1/(x-3)-1/(x-2)-1/(x-3)+1/(x-1)+1/(x-2)-1/(x-1)
=0

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