Question

tìm x,y thỏa mãn

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

Answer 1

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

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

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

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

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

\(\Rightarrow5x+6=2011\)

\(\Rightarrow5x=2011-6\)

\(\Rightarrow5x=2005\)

\(\Rightarrow x=401\)