1/2=1/1x2=1/1-1/2,1/6=1/2x3=1/2-1/3,1/12=1/3x4=1/3-1/4

来源：百度知道 编辑：UC知道 时间：2024/05/22 10:54:32
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.利用你得出的结论,计算:1/(a-1)(a-2) +1/(a-2)(a-3) +1/(a-3)(a-4) +1/(a-4)(a-5)

2.计算：2c/b的2次方-c的2次方 -1/b+c + 1/c-b

这是谁出的题啊！

1.1/n（n+1)=1/n-1/(n+1)
2.1/(a-1)(a-2) +1/(a-2)(a-3) +1/(a-3)(a-4) +1/(a-4)(a-5)
=1/（a-2)-1/(a-1)+1/(a-3)-1/(a-2)+1/(a-4)-1/(a-3)+1/(a-5)-1/(a-4)
=1/(a-5)-1/(a-1)=4/(a-5)(a-1)
3.2c/(b*b-c*c)-1/(b+c)+1/(c-b)=2c/(b*b-c*c)-2b/(b*b-c*c)
=-2/(b+c)

1.1/n（n+1)=1/n-1/(n+1)

2.原式得1/（a-2)-1/(a-1)+1/(a-3)-1/(a-2)+1/(a-4)-1/(a-3)+1/(a-5)-1/(a-4)
=1/(a-5)-1/(a-1)
=4/(a-5)(a-1)

3.2c/(b^2-c^2)-1/(b+c)+1/(c-b)
=2c/(b+c)(b-c)-1/(b+c)-1/(b-c)
=2c/(b+c)(b-c)-[1/(b+c)+1/(b-c)]
=2c/(b+c)(b-c)-2b/(b+c)(b-c)
=2(c-b)/(b+c)(b-c)
=-2/(b+c)