Ta có: \(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=5750\)

\(\Leftrightarrow100x+5050=5750\)

\(\Leftrightarrow100x=700\)

hay x=7

x=7

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(x+1)+(x+2)+...+(x+100)=5750

(x+x+...+x)+(1+2+3+...+100)=5750

100x+5050=5750

100x=5750-5050

100x=700

x=700/100

x=7

\(\Leftrightarrow100x+5050=5750\)

hay x=7

(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 +...+ 100) = 5750

100x + 5050 = 5750

100x = 5750 - 5050

100x = 700

x = 700 : 100

x = 7

=>100x+5050=5750

=>100x=700

=>x=7

x(x+1)+(x+2)+(x+3)+...+(x+100)=5750

=> (x+x+x+x+...+x)+(1+2+3+...+100)=5750

=> 101x+5050=5750

101x = 5750-5050

101x = 700

x = 700 : 101

x = 700/101

vậy kết quả bằng bao nhiêu vậy?

x+x+x+...x+ 1+2+3+...100 = 5750

100.x + 101.50 = 5750

100.x = 5757-5050

100.x = 700

x = 700: 100

x = 7

(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

                                            \(x100+\left(101.50\right)=5750\)

                                                      \(x100+5050=5750\)

                                                                        \(x100=5750-5050\)

                                                                        \(x100=700\)

                                                                                \(x=700:100=7\)

Ta có:

(x + 1) + (x + 2) + ... +(x + 100) = 5750

100x + 1 +2 + 3 + 4 + 5 +... + 100= 5750

100x + \(\frac{1+100}{2}\) = 5750

100x + 1+ 100 = 11500

100x = 11399

x = 113,99

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 100 ) =5750

( x + x + x + ... + x ) + ( 1 + 2 + 3 + ... + 100 ) = 5750

100x + 5050 = 5750

100x = 5750 - 5050

100x = 700

x = 700 : 100

x = 7

100x+5050=5750
100x=700
x=7

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5750\)

\(\Leftrightarrow\left(x+x+x+....+x\right)+\left(1+2+3+...+100\right)=5750\)

\(\Leftrightarrow100x+\frac{\left(1+100\right).100}{2}=5750\)

\(\Leftrightarrow100x+5050=5750\)

\(\Leftrightarrow100x=700\)

\(\Leftrightarrow x=7\)