\(\frac{2005\times2004-1}{2003\times2005+2004}=\frac{2005\times2003+2005-1}{2003\times2005+2004}=\frac{2005\times2003+2004}{2003\times2005+2004}=1\)

\(\frac{2005\cdot2004-1}{2003\cdot2005+2004}\)

\(=\frac{2005\cdot\left(2003+1\right)-1}{2003\cdot2005+2004}\)

\(=\frac{2005\cdot2003+2005-1}{2003\cdot2005+2004}\)

\(=\frac{2005\cdot2003+2004}{2003\cdot2005+2004}\)

\(=1\)

2005 x 2004 - 1 / 2003 × 2005 + 2004

= 2005 × (2003 + 1) - 1 / 2003 × 2005 + 2004

= 2005 × 2003 + (2005 - 1) / 2003 × 2005 + 2004

= 2005 × 2003 + 2004 / 2003 × 2005 + 2004

= 1

\(\frac{2005\times2004-1}{2003\times2005+2004}\)

\(=\frac{2005\times\left(2003+1\right)-1}{2003\times2005+2004}\)

\(=\frac{2005\times2003+\left(2005-1\right)}{2003\times2005+2004}\)

\(=\frac{2005\times2003+2004}{2003\times2005+2004}\)

\(\frac{2005x2004-1}{2003x2005+2004}\)=\(\frac{4018019}{4018019}\)= 1

                       Bài giải

\(\frac{2005\text{ x }2004-1}{2003\text{ x }2005+2004}=\frac{2005\text{ x }2004-1}{2003\text{ x }2005+2005-1}=\frac{2005\text{ x }2004-1}{2005\text{ x }2004-1}=1\)

\(\frac{2005\times2004-1}{2003\times2005+2004}\)\(=\)\(\frac{2005\times\left(2003+1\right)-1}{2003\times2005+2004}\)\(=\)\(\frac{2005\times2003+2005-1}{2003\times2005+20042}\)\(=\)\(\frac{2005\times2003+2004}{2003\times2005+2004}\)\(=\)1

y=\(\frac{2006x2005-1}{2004x2006+2005}=\frac{2006x2005-1}{\left(2005-1\right)x2006+2005}=\frac{2006x2005-1}{2005x2006-2006+2005}=\frac{2006x2005-1}{2005x2006-1}=1\)

Ta có: \(\frac{2004\cdot2007+6}{2005\cdot2005+2009}=\frac{\left(2005-1\right)\cdot2007+6}{2005\cdot2005+2009}=\frac{2005\cdot2007-1\cdot2007+6}{2005\cdot2005+2009}=\frac{2005\cdot2007-2007+6}{2005\cdot2005+2009}\)

\(=\frac{\text{2005 x (2005 + 2) - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\frac{\text{2005 x 2005 + 2005 x 2 - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\frac{\text{2005 x 2005 + 4010 - 2007 + 6}}{\text{2005 x 2005 + 2009}}=\text{ }\frac{\text{2005 x 2005 + 2009}}{\text{2005 x 2005 + 2009}}=1\)

\(\frac{2004\times2007+6}{2005\times2005+2009}\)

\(=\frac{2004\times2007-2007+6}{2005\times2005+2009}\)

\(=\frac{2005\times2005+2005+2005-2007+6}{2005\times2005+2009}\)

\(=\frac{2005\times2005+2009}{2005\times2005+2009}=1\)

Giúp mình nha

Ta có: 1/ 2001 . 2003 = 1/2001 - 1/2003...

=> 1/2001 - 1/2003 + 1/2003 - 1/2005 + 1/2005 - 1/2007 + ... +1/2009 - 1/2011 +1/2011 - 1/2013

= 1/2001 - 1/2013

= 4/ 1342671

\(\frac{1}{2001\times2003}\)+\(\frac{1}{2003\times2005}\)+\(\frac{1}{2005\times2007}\)+........+\(\frac{1}{2009\times2011}\)+\(\frac{1}{2011\times2013}\)

=\(\frac{1}{2001}-\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2007}\)+........+\(\frac{1}{2009}\)-\(\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2013}\)

=\(\frac{1}{2001}\)-\(\frac{1}{2013}\)

=\(\frac{2013}{4028013}-\frac{2001}{4028013}\)=\(\frac{2}{4028013}\)

\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{2004\cdot2005}+\frac{1}{2005\cdot2006}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2006}\)

\(A=1-\frac{1}{2006}=\frac{2005}{2006}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2005.2006}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2005}-\frac{1}{2006}\)

\(\Rightarrow A=1-\frac{1}{2006}\)

\(\Rightarrow A=\frac{2005}{2006}\)

\(1)A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2004.2005}+\frac{1}{2005.2006}\)

\(\implies A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2006}\)

\(\implies A=1-\frac{1}{2006}\)

\(\implies A=\frac{2005}{2006}\)