\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(x+1+x+2+...+x+100=5750\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
Số số hạng là \(\left(100-1\right)\div1+1=100\) số hạng
=> Có 100 số x
Tổng là \(\left(100+1\right)\times100\div2=5050\)
=> \(x\times100+5050=5750\)
\(x\times100=5750-5050\)
\(x\times100=700\)
\(x=700\div100\)
\(x=7\)
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(\Rightarrow100x+\left(1+2+...100\right)=5750\)
\(\Rightarrow100x+\dfrac{100.\left(100+1\right)}{2}=5750\)
\(\Rightarrow100x+50.101=5750\)
\(\Rightarrow100x+5050=5750\)
\(\Rightarrow100x=5750-5050\)
\(\Rightarrow100x=700\)
\(\Rightarrow x=7\)