(x + 1) + (x + 2) + (x + 3) + ... + (x + 100) = 5750
=> x + 1 + x + 2 + x + 3 + ... + x + 100 = 5750
=> (x + x + x + .... + x) + (1 + 2 + 3 + 4 + ... + 100) = 5750 (100 số hạng x)
=> 100x + \(\left[\left(100-1\right):1+1\right].\left(\frac{100+1}{2}\right)\) = 5750
=> 100x + \(100.\frac{101}{2}\)= 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7
#)Giải :
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+...+100\right)=5750\)(mỗi cặp có 100 số hạng)
\(\Leftrightarrow x\times100+5050=5750\)
\(\Leftrightarrow x\times100=700\)
\(\Leftrightarrow x=7\)
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)
\(x100+\left(1+2+3+...+100\right)=5750\)
\(x100+\left(101+101+...+101\right)=5750\)có 50 số 101
\(x100+\left(101.50\right)=5750\)
\(x100+5050=5750\)
\(x100=5750-5050\)
\(x100=700\)
\(x=700:100=7\)
