Ta có : \(\dfrac{1}{2006.2005}+....+\dfrac{1}{3.2}+\dfrac{1}{2.1}\)

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

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{2005}-\dfrac{1}{2006}\)

\(=1-\dfrac{1}{2006}=\dfrac{2005}{2006}\)

Bạn ơi cho mình hỏi từ sau chỗ \(\frac{1}{2004.2003}\)là dấu trừ hết ạ? Nếu là dấu cộng thì mình làm được :33

đúng rồi bạn ơi thế mới khó

Bạn làm được ko vậy ko thì đừng cố quá

A = 7/7.17 + 7/17.27 + 7/27.37 + ............ +7/1997.2007

A=7/10 ( 10/7.17 + 10/17.27 + 10/27.37 + ................+10/1997.2007)

A= 7/10  ( 1/7 -1/17 + 1/17 - 1/27 + 1/27 - 1/37 +...............+ 1/1997 - 1/2007)

A= 7/10 (1/7 - 1/2007)

A= 7/10 . 2000/14049

A=200/2007

bây h mk có vc rùi tích đúng nha tối mk lm típ cho

\(\frac{2005.2004-1}{2003.2005+2004}=\frac{2005.\left(2003+1\right)-1}{2003.2005+2004}=\frac{2005.2003+2005-1}{2005.2003+2004}=\frac{2005.2003+2004}{2005.2003+2004}=1\)

\(\dfrac{1}{2014}-\dfrac{1}{2014.2013}-\dfrac{1}{2013.2012}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}=\dfrac{1}{2014}-\left(\dfrac{1}{2013.2014}+\dfrac{1}{2012.2013}+...+\dfrac{1}{2.3}+\dfrac{1}{1.2}\right)=\dfrac{1}{2014}-\left(\dfrac{1}{2013}-\dfrac{1}{2014}+\dfrac{1}{2012}-\dfrac{1}{2013}+...+\dfrac{1}{2}-\dfrac{1}{3}+1-\dfrac{1}{2}\right)=\dfrac{1}{2014}-\left(1-\dfrac{1}{2014}\right)=\dfrac{1}{2014}-\dfrac{2013}{2014}=-\dfrac{1006}{1007}\)

=1/2014-(1/1*2+1/2*3+...+1/2013*2014)

=1/2014-(1-1/2+1/2-1/3+...+1/2013-1/2014)

=1/2014-1+1/2014

=1/1007-1=-1006/1007

\(\dfrac{1}{2003.2002}-\dfrac{1}{2002.2001}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

= \(\dfrac{1}{2003.2002}-\left(\dfrac{1}{2002.2001}+...+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\)

= \(\dfrac{1}{2003.2002}-\left(\dfrac{1}{2002}-\dfrac{1}{2001}+...+\dfrac{1}{3}-\dfrac{1}{2}+\dfrac{1}{2}-1\right)\)

= \(\dfrac{1}{2003.2002}-\dfrac{1}{2002}+1\)

= \(\dfrac{1-2003+2003.2002}{2003.2002}\)

= \(1-\dfrac{2002}{2003.2002}=1-\dfrac{1}{2003}\) = \(\dfrac{2002}{2003}\)