Được chưa bây giờ tic đúng đi

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}=\frac{996}{997}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{996}{997}\)

\(1-\frac{1}{x+1}=\frac{996}{997}\)

         \(\frac{1}{x+1}=1-\frac{996}{997}\)

         \(\frac{1}{x+1}=\frac{1}{997}\)

\(\Rightarrow x+1=997\)

               \(x=997-1\)

               \(x=996\)

Ấm đầu hả phải tic bài làm chứ 

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x\left(x+1\right)}=\frac{996}{997}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{996}{997}\)

\(1-\frac{1}{x+1}=\frac{996}{997}\)

\(\frac{1}{x+1}=1-\frac{996}{997}=\frac{1}{997}\)

\(\Rightarrow x+1=997\Rightarrow x=996\)

Vậy \(x=996\)

`1 + 2 - 3 - 4 + ....+ 994 -995 - 996 + 997 + 998 `

`= 1 + (2 - 3 - 4 +5) +....+ (994 -995 - 996 + 997) + 998 `

`= 1 + 0 + ...+ 0 + 998`

`= 1 + 998`

`= 999`

Đề :

`1+2-3-4+...+994-995-996+997+998`

\(\Rightarrow\) `1+(2-3-4+5)+...+(994-995-996+997)+998`

\(\Rightarrow\) `1+0+...+0+998`

\(\Rightarrow\) `1+998`

\(\Rightarrow\) `999`

@Nae