Question

求解！！急急急急！

已知：1/(1*2)+1/(2*3)+1/(3*4)+……+1/n(n+1)=1-1/2+1/2-1/3+1/3-1/4+…+ 1/n-1/(n+1)
如何化简1/(x+1)+1/[x(x+1)]+1/[(x+1)(x+2)]+…+1/[(x+2005)(x+2006)]?

求解下列分式方程：
1/[x(x+3)]+1/[(x+3)(x+6)]-1/3x=1问题补充：

求解！！！！急急急急急急！！！

Answer 1

(1)1/(x+1)+1/[x(x+1)]+1/[(x+1)(x+2)]+…+1/[(x+2005)(x+2006)]
=1/(x+1)+1/x-1/(x+1)+1/(x+1)-1/(x+2)+…+1/(x+2005)-1/(x+2006)
=1/(x+1)+1/x-1/(x+2006)
(2)1/[x(x+3)]+1/[(x+3)(x+6)]-1/3x=1
1/x-1/(x+3)+1/(x+3)-1/(x+6)-1/x=3
-1/(x+6)=3
x=-19/3