\(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right).5x+6}=\frac{2005}{2006}\)
\(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+....+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(1-\frac{1}{5x+6}=\frac{2005}{2006}\)
\(\frac{1}{5x+6}=1-\frac{2005}{2006}\)
\(\frac{1}{5x+6}=\frac{1}{2006}\)
=>5x+6 = 2006
=>5x = 2000
=>x = 400
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
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