观察下列各式1/2=1-1/2；1/6=1/2*3=1/2-1/3；1/12=1/3*4=1/3-1/4 计算1/2+1/6+1/12……+1/9+1/110。

观察下列各式1\/2=1-1\/2;1\/6=1\/2*3=1\/2-1\/3;1\/12=1\/3*4=1\/3-1\/4...
1\/2+1\/6+1\/12……+1\/90+1\/110 =1\/1*2+1\/2*3+1\/3*4+...1\/9*10+1\/10*11 =1-1\/2+1\/2-1\/3+...+1\/9-1\/10+1\/10-1\/11 =1-1\/11 =10\/11 如有不明白，可以追问！！谢谢采纳！

观察下列各式:1\/1×2=1-1\/2;1\/2×3=1\/2-1\/3;1\/3×4=1\/3-1\/4,···
解：(1) 1\/n（n+1）=1\/n-1\/(n+1)(2)1\/2+1\/6+1\/12+···+1\/24=(1-1\/2)+(1\/2-1\/3)+(1\/3-1\/4)+...+(15-1\/16)=1-1\/2+1\/2-1\/3...+1\/15-1\/16 =1-1\/16 =15\/16

观察下列各式,1\/6=1\/2*3=1\/2-1\/3;1\/12=1\/3*4=1\/3-1\/4:1\/20=1\/4*5=...
1\/（x-2)（x-3)-2\/(x-1)(x-3)+1\/(x-1)(x-2)=1\/（x-2)（x-3)-1\/(x-1)(x-3)+)-1\/(x-1)(x-3)+1\/(x-1)(x-2)=1\/（x-3)*(1\/（x-2)-1\/(x-1))+1\/(x-1)*(1\/(x-2)-1\/(x-3))=-1\/（（x-3)*（（x-2)(x-1))）+1\/（（x-3)*（（x-2...

观察下列各式,1\/1*2=1-1\/2 1\/2*3=1\/2-1\/3,1\/3*4=1\/3-1\/4
化简成1\/(x-1)-1\/x+1\/(x-2)-1\/(x-1)+…+1\/(x-10)-1\/(x-9)=5\/12 1\/(x-10)-1\/x=5\/12 10\/(x(x-10))=5\/12 x=12

...1\/6=1\/2×3=1\/2-1\/3 1\/12=1\/3×4=1\/3-1\/4 1\/20=1\/4×5=1\/4-1\/5...
(x-3) = 1\/4 * 1\/ (x\/2-1\/2)(x\/2-3\/2) = 1\/4 * ( 1\/(x\/2 - 3\/2) - 1\/(x\/2-1\/2) ) = 1\/2 * ( 1\/(x-3) - 1\/(x-1) ); 1\/n(n+1)=1\/n-1\/(n+1)化简＝（n+3）(n+4)+(n+1)(n+4)+(n+1)(n+2)\/(n+1)(n+2)（n+3）(n+4)=(n+...

观察下列等式:1\/1*2=1-1\/2,1\/2*3=1\/2-1\/3,1\/3*4=1\/3-1\/4,将以上三个...
解：这是分式相消的思想！观察结果：注意：1\/1*2 = (2-1)\/1*2 = 2\/1*2 - 1\/1*2 = 1\/1 - 1\/2 1\/2*3 = (3-2)\/2*3 = 3\/2*3 - 2\/2*3 = 1\/2 - 1\/3 1\/3*4 = (4-3)\/3*4 = 4\/3*4 - 3\/3*4 = 1\/3 - 1\/4 上述各式相加：左边=1\/1*2+1\/2*3+...

观察下列各式,1\/1*2=1-1\/2 1\/2*3=1\/2-1\/3,1\/3*4=1\/3-1\/4
原式=1\/1*2+1\/2*3+…+1\/11*12 =1-1\/2+1\/2-1\/3+…+1\/11-1\/12 =1-1\/12 =11\/12

观察下列各式,1\/6=1\/2*3=1\/2-1\/3;1\/12=1\/3*4=1\/3-1\/4:1\/20=1\/4*5=...
根据规律方程=1\/(x-2)-1\/(x-3)-[1\/(x-1)-1\/(x-3)]+1\/(x-1)-1\/(x-2)=0

观察下列各式,1\/1*2=1-1\/2 1\/2*3=1\/2-1\/3,1\/3*4=1\/3-1\/4
因为1\/n(n+2)=[1\/n-1\/(n+2)]\/2 所以 1\/2*4+1\/4*6+1\/6*8+...+1\/98*100 =1\/2*(1\/2-1\/4)+1\/2*(1\/4-1\/6)+1\/2*(1\/6-1\/8)+...+1\/2*(1\/98-1\/100)=1\/2*(1\/2-1\/4+1\/4-1\/6+1\/6-1\/8+...+1\/98-1\/100)=1\/2*(1\/2-1\/100)=49\/200.

观察下列等式1\/1×2=1-1\/2,1\/2×3=1\/2-1\/3,1\/3×4=1\/3-1\/4,将以上三...
题中有个地方有错：（2）1\/1×2+1\/2×3+1\/3×4+...+1\/n（n-1）= 如果用省略号，默认数列满足通式，显然你这儿n-1小于n，格式不对，给你改成（2）1\/1×2+1\/2×3+1\/3×4+...+1\/[(n-1)n]计算的 (1) 1\/[n(n+1)]= 1\/n-1\/(n+1)(2) 1\/1×2+1\/2×3+...