Question

Tìm x : 

\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{x\left(x+1\right)}=\frac{75}{76}\)

 \(\left(x-1\right).\left(x-2\right)=0\)

Answer 1

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}=\frac{75}{76}\)

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{75}{76}\)

\(\frac{1}{1}-\frac{1}{x+1}=\frac{75}{76}\)

\(\frac{1}{x+1}=1-\frac{75}{76}\)

\(\frac{1}{x+1}=\frac{1}{76}\)

\(\Rightarrow x+1=76\)

\(x=75\)

vậy \(x=75\)

Answer 2

(x+1).(x+2)=0

\(\hept{\begin{cases}x+1=0\\x+2=0\end{cases}}\)

\(\hept{\begin{cases}x=-1\\x=-2\end{cases}}\)

vậy x{-1;-2}

Answer 3

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}=\frac{75}{76}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{75}{76}\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{75}{76}\)

\(\Leftrightarrow\frac{1}{x+1}=1-\frac{75}{76}=\frac{1}{76}\)

\(\Leftrightarrow x+1=76\Rightarrow x=75\)

\(\left(x-1\right).\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)