\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{x.\left(x+1\right)}=\frac{88}{100}\)
\(\Leftrightarrow\frac{2-1}{1.2}+\frac{3-2}{2.3}+...+\frac{\left(x+1\right)-x}{x.\left(x+1\right)}=\frac{88}{100}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{\left(x+1\right)}=\frac{88}{100}\)
\(\Leftrightarrow1-\frac{1}{\left(x+1\right)}=\frac{88}{100}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)}=1-\frac{88}{100}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)}=\frac{3}{25}\)
\(\Leftrightarrow\left(x+1\right)\cdot3=1\cdot25\)
\(\Leftrightarrow x+1=\frac{25}{3}\)
\(\Leftrightarrow x=\frac{25}{3}-1=\frac{22}{3}\)
\(\frac{1}{1.2} +\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{88}{100}\)
<=>\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{88}{100}\)
<=>\(1-\frac{1}{x+1}=\frac{88}{100}\)<=>\(\frac{x}{x+1}=\frac{88}{100}\Leftrightarrow100x=88x+88\Leftrightarrow12x=88\Leftrightarrow x=\frac{22}{3}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x.\left(x+1\right)}=\frac{88}{100}\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}+\frac{1}{x+1}=\frac{88}{100}\)
\(\Rightarrow1-\frac{1}{x+1}=\frac{88}{100}\)
\(\Rightarrow\frac{1}{x+1}=1-\frac{88}{100}\)
\(\Rightarrow\frac{1}{x+1}=\frac{100}{100}-\frac{88}{100}\)
\(\Rightarrow\frac{1}{x+1}=\frac{3}{25}\)
\(\Rightarrow\frac{3}{3\left(x+1\right)}=\frac{3}{25}\)
\(\Rightarrow3\left(x+1\right)=25\)
\(\Rightarrow\left(x+1\right)=25:3\)
\(\Rightarrow x+1=\frac{25}{3}\)
\(\Rightarrow x=\frac{25}{3}-\frac{3}{3}\)
\(\Rightarrow x=\frac{22}{3}\)
\(KL:x=\frac{22}{3}\)
k cho mk nha !
