Ta có : $\frac{1}{21}$+$\frac{1}{28}$+...+$\frac{2}{x(x+1)}$=$\frac{2}{42}$+$\frac{2}{56}$+...+$\frac{2}{x(x+1)}$=2($\frac{1}{6.7}$+$\frac{1}{7.8}$+...+$\frac{1}{x(x+1)}$)= 2($\frac{1}{6}$-$\frac{1}{x+1}$)=$\frac{2}{9}$$\Leftrightarrow$$\frac{1}{6}$-$\frac{1}{x+1}$=$\frac{1}{9}$$\Leftrightarrow$$\frac{1}{x+1}$=$\frac{1}{18}$$\Leftrightarrow$x+1=18$\Leftrightarrow$x=17
Ta có : $\frac{1}{21}$+$\frac{1}{28}$+...+$\frac{2}{x(x+1)}$=$\frac{2}{42}$+$\frac{2}{56}$+...+$\frac{2}{x(x+1)}$=2($\frac{1}{6.7}$+$\frac{1}{7.8}$+...+$\frac{1}{x(x+1)}$)= 2($\frac{1}{6}$-$\frac{1}{x+1}$)=$\frac{2}{9}$Phương trình cần giải đó
Ta có : $\frac{1}{21}$+$\frac{1}{28}$+...+$\frac{2}{x(x+1)}$=$\frac{2}{42}$+$\frac{2}{56}$+...+$\frac{2}{x(x+1)}$=2($\frac{1}{6.7}$+$\frac{1}{7.8}$+...+$\frac{1}{x(x+1)}$)= 2($\frac{1}{6}$-$\frac{1}{x+1}$)=$\frac{2}{9}$
$\Leftrigh
tarrow$$\frac{1}{6}$-$\frac{1}{x+1}$=$\frac{1}{9}$$\Leftrig
ht
ar
row$$\frac
{1}{x+1}$=$\frac{1}{18}$$\Leftri
ghtarrow$x+1=18$\Leftri
ghtarrow$x=17