x= 0

vi x ko co gia tri

Viết nhầm 

100x+5050=102x

100x+5050=100x+2x

=>2x=5050

x=5050/2

x=2525

(x + 1) + (x + 2) + ... + (x + 100) = 102x

x + x + x + ... + x + 1 + 2 + ... + 100 = 102x

100x + (100 + 1) x 100 : 2 = 102x

102x - 100x = 5050

2x = 5050

x = 2525

(x + 1) + (x + 2) + (x + 3) + (x + 4 ) + ... + (x + 99) + (x + 100) = 102x

(x+x+x+...+x)+(1+2+3+4+...+100) = 102x

100x + 5050 = 102x

<=>102x-100x=5050

(102-100)x=5050

2x=5050

x=5050:2

x=2525

sửa :

Số các số tự nhiên từ 1 đến 100 là:

   [100-1] : 1 +1 =100 [số]

(x-1)+(x-2)+(x-3)+(x-4)+...+(x-100)=205550

=> 100.x -[1+2+3+..+100] = 205550

=> 100.x - 100x101 : 2 = 205550

=> 100.x -5050= 205550

=> 100.x = 210600 => x= 2106

Ta có : 

\(\frac{x+1}{100}+\frac{x+2}{99}=\frac{x+3}{98}+\frac{x+4}{97}\)

\(\Leftrightarrow\)\(\left(\frac{x+1}{100}+1\right)+\left(\frac{x+2}{99}+1\right)=\left(\frac{x+3}{98}+1\right)+\left(\frac{x+4}{97}+1\right)\)

\(\Leftrightarrow\)\(\frac{x+101}{100}+\frac{x+101}{99}=\frac{x+101}{98}+\frac{x+101}{97}\)

\(\Leftrightarrow\)\(\frac{x+101}{100}+\frac{x+101}{99}-\frac{x+101}{98}-\frac{x+101}{97}=0\)

\(\Leftrightarrow\)\(\left(x+101\right)\left(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\right)=0\)

Vì \(\frac{1}{100}+\frac{1}{99}-\frac{1}{98}-\frac{1}{97}\ne0\)

Nên \(x+101=0\)

\(\Rightarrow\)\(x=-101\)

Vậy \(x=-101\)

Chúc bạn học tốt ~ 

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gửi câu hỏi 20 giây nhớ ra

(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 = 700 
x = 700 : 100 = 7

 x + 1 + x + 2 + .. + x + 100 = 5750

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

=> 100x + 5050 = 5750

=> 100x             = 5750 - 5050

=> 100x             = 700 

=> 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 = 700

=> x = 700 : 100 = 7