ta có:1/21+1/28+1/36+...+1/x.(x+1)=2/9
=>1/(3.7)+1/(4.7)+1/(4.9)+...+2/x(x+1)=2/9
=>2/(6.7)+2/(7.8)+2/(8.9)+...+2/x(x+1)=2/9
=>2.[1/6-1/(x+1)]=2/9
=>1/6-1/(x+1)=1/9
=>1/(x+1)=1/18
=>x+1=18
=>x=17.
Vậy x = 17.
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+....+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2}{9}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+.....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)
\(\Leftrightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\Leftrightarrow\frac{1}{x+1}=\frac{1}{18}\Rightarrow x=18-1=17\)
Ta có:
\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{1}{x.\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow\frac{1}{3.7}+\frac{1}{7.4}+\frac{1}{4.9}+...+\frac{1}{x.\left(x+1\right)}=\frac{2}{9}\)
\(\Rightarrow2.\left(\frac{1}{3.7}+\frac{1}{7.4}+\frac{1}{4.9}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{1}{9}\)
\(\Rightarrow\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x.\left(x+1\right)}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x-1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{x-1}=\frac{1}{9}\)
\(\Rightarrow\frac{1}{x-1}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\)
\(\Leftrightarrow x-1=18\Rightarrow x=17\)