\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{x\left(x+1\right)\left(x+2\right)}=\frac{1998}{1999}\)
\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}\right)=\frac{1998}{1999}\)
\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)=\frac{1998}{1999}\)
\(\Leftrightarrow\frac{1}{1.2}-\frac{1}{\left(x+1\right)\left(x+2\right)}=\frac{1998}{1999}\div\frac{1}{2}\)
\(\Leftrightarrow\frac{1}{1.2}-\frac{1}{\left(x+1\right)\left(x+2\right)}=\frac{3996}{1999}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)\left(x+2\right)}=\frac{1}{1.2}-\frac{3996}{1999}\)
\(\Leftrightarrow\frac{1}{\left(x+1\right)\left(x+2\right)}=\frac{-5993}{3998}\)
Như kiểu đề sai hay sao í
