\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).5x+6}=\frac{2005}{2006}\)

\(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(1-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\frac{1}{5x+6}=1-\frac{2005}{2006}\)

\(\frac{1}{5x+6}=\frac{1}{2006}\)

=>5x+6 = 2006

=>5x = 2000

=>x = 400

x = 400 nha bạn

                       Bài làm :

Ta có :

\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).\left(5x+6\right)}=\frac{2005}{2006}\)

\(\Leftrightarrow\frac{6-1}{1.6}+\frac{11-6}{6.11}+...+\frac{5x+6-5x-1}{\left(5x+1\right).\left(5x+6\right)}=\frac{2005}{2006}\)

\(\Leftrightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Leftrightarrow1-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Leftrightarrow\frac{1}{5x+6}=1-\frac{2005}{2006}\)

\(\Leftrightarrow\frac{1}{5x+6}=\frac{1}{2006}\)

\(\Leftrightarrow1.2006=\left(5x+6\right).1\)

\(\Leftrightarrow2006=5x+6\)

\(\Leftrightarrow5x=2006-6\)

\(\Leftrightarrow5x=2000\)

\(\Leftrightarrow x=2000\div5=400\)

Vậy x=400

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Ta có công thức \(\frac{a}{b.c}=\frac{a}{c-b}.\left(\frac{1}{b}-\frac{1}{c}\right)\)

Dựa vào công thức trên, ta có:

\(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Rightarrow1-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\Rightarrow\)\(\frac{1}{5x+6}=1-\frac{2005}{2006}=\frac{1}{2006}\)

\(\Rightarrow\)\(5x+6=2006\Rightarrow x=400\)

chắc chắn, ủng hộ mink nha

         \(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).\left(5x+6\right)}=\frac{2005}{2006}\)

\(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(1-\frac{1}{5x+6}=\frac{2005}{2006}\)

        \(\frac{1}{5x+6}=1-\frac{2005}{2006}\)

        \(\frac{1}{5x+6}=\frac{1}{2006}\)

\(\Rightarrow5x+6=2006\)

             \(5x=2006-6\)

            \(5x=2000\)

               \(x=2000:5\)

               \(x=400\)

1-1/6+1/6-1/11+...+1/5x+1-1/5x+6=2005/2006

1-1/5x+6=1-1/2006

5x+6=2006

5x=2000

x=400

\(1-\frac{1}{5x+6}=\frac{2005}{2006}\Leftrightarrow5x+6=2006\Leftrightarrow x=400\)

x=400 

\(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(\frac{1}{1}-\frac{1}{5x+6}=\frac{2005}{2006}\)

\(-\frac{1}{5x+6}=\frac{2005}{2006}-\frac{1}{1}\)

\(-\frac{1}{5x+6}=-\frac{1}{2006}\)

\(\Rightarrow\frac{1}{5x+6}=\frac{1}{2006}\)

⇒ 5x + 6 = 2006

⇒ 5x = 2006 - 6 = 2000

⇒ x = 2000 : 5 = 400

Vậy x = 400

Ta có:

\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).\left(5x+6\right)}\)

\(=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}\)

\(=1-\frac{1}{5x+6}\)

\(=\frac{5x+5}{5x+6}=\frac{2010}{2011}\)

\(\Rightarrow5x+5=2010\)

\(\Rightarrow5x=2010-5=2005\)

\(\Rightarrow x=2005:5=401\)

Vậy x=401

=> 1 - 1/6 + 1/6 - 1/11 + ......+ 1/5x+1 - 1/5x + 6 = 2010/2011

=> 1 - 1/5x+6 = 2010/2011

=> 1/5x+6 = 1 - 2010/2011

=> 1/5x + 6 = 2009/2011

=> ...........................Còn lại bạn tự làm nha!

Ai k mk mk k lại !!!

\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).\left(5x+6\right)}=\frac{2010}{2011}\)

\(\Rightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2010}{2011}\)

\(\Rightarrow1-\frac{1}{5x+6}=\frac{2010}{2011}\)

\(\Rightarrow\frac{1}{5x+6}=1-\frac{2010}{2011}\)

\(\Rightarrow\frac{1}{5x+6}=\frac{1}{2011}\)

\(\Rightarrow5x+6=2011\)

\(\Rightarrow5x=2011-6\)

\(\Rightarrow5x=2005\)

\(\Rightarrow x=401\)