观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/26 16:45:33

观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1); 1/(x-2)(x-3)=1/(x-3)-1/(x-2);
观察下列关系式:1/(x-1)(x-2)=1/(x-2)-1/(x-1);
1/(x-2)(x-3)=1/(x-3)-1/(x-2);
1/(x-3)(x-4)=1/(x-4)-1/(x-3);
1/(x-4)(x-5)=1/(x-5)-1/(x-4);
.
(1)你可以归纳出一般结论是____________.
(2)请利用上述结论计算：1/(x+1)+1/(x-1)(x+2)+1/(x-2)(x-3)+...+1/(x-99)(x-100).

可以归纳出一般的结论是：相邻的两个自然数积的倒数等于这两个自然数的倒数之差!
1/(x-1)(x-2)+1/(x-2)(x-3)+……+1/(x-99)(x-100)
=1/(x-1)-1/(x-2)+1/(x-2)-1/(x-3)+……+1/(x-99)-1/(x-100)
=1/(x-1)-1/(x-100)
=[(x-100)-(x-1)]/[(x-1)(x-100)]
=-99/[(x-1)(x-100)]

x^5+x^4 = (x^3-x)(x^2+x+1)+x^2+x (观察下式:(x-1)(x+1)=x^2-1; (x-1)(x^2+x+1)=x^3-1; (x-1)(x^3+x^2+ 观察下列各式：（x-1）（x+1）=xˆ2-1 （x-1）（xˆ2+x+1）=xˆ3-1 解方程x/(x-2)=2x/(x-3)+(1-x)/(x-5x+6) x-1)(X-2)(x-3)...(x-50)+x(x-2)(X-3)...(X-50)+...+x(x-1)(x-2) x^4+x^3+x^2+x+1=0,x^2006+x^2005+x^2004+x^2003+x^2002 谁就是聪明人观察下列各式：（x-1）（x+1）=x^2-1（x-1）（x^2+x+1）=x^3-1（x-1）（x^3+x 已知f(x)满足关系式f(x)+2f(1/x)=3x,求f(x) 若f(x)满足关系式 f(x)+2f(1/x)=3x,求f(x)的解析式 x+2/x+1-x+3/x+2-x+4/x+3+x+5/x+4 x/x平方-x+2=2x/x+1 1+x+x^2+x^3+.+x^99+x^100