Giải các phương trình sau: \(\frac{1}{2x-2006}\)+\(\frac{1}{3-2007x}\)+\(\frac{1}{2006x+2005}\)=\(\frac{1}{x+2}\)

giải phương trình :

\(\frac{x^2+2006x-1}{2006}+\frac{x^2+2006x-2}{2005}+...+\frac{x^2+2006x-7}{2000}=\frac{x^2+2006x-8}{1999}+...+\frac{x^2+2006x-14}{1993}\)

Rút gọn các biểu thức sau

A= x^6-2007x^5+2007x^4-2007x^3+2007x^2-2007x+2007 với x=2006

B= x^10-2006x^9+2006x^8-2006x^7+...+2006x^2-2006 với x=2005

CM : \(\frac{\sqrt{x-2005}-1}{x-2005}+\frac{\sqrt{x-2006}-1}{x-2006}=\frac{1}{2}\)

Tinh A = \(\frac{\frac{2006}{1}+\frac{2006}{2}+\frac{2006}{3}+........\frac{2006}{2006}+\frac{2006}{2007}}{\frac{1}{2006}+\frac{2}{2005}+\frac{3}{2004}+.........+\frac{2005}{2}+\frac{2006}{1}}\)

cho xyz=2006 . chung minh rang \(\frac{2006x}{xy+2006x+2006}+\frac{y}{yz+y+2006}+\frac{z}{xz+z+1}=1\)

CM \(\frac{1}{2}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{2006\sqrt{2005}}< 2\)

cm P=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2006}<\frac{2}{5}\)