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2+4+6+8+10+...+2500
= (2+2500) x 625
= 2502 x 625 = 1563750 = 1250 x 1251
Vậy x=1250
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1) + (x+2) +....+(x+100) = 5050
100 x X + ((100+1) x 100 : 2) = 5050
100 x X + 5050 = 5050
100 x X = 0
=> x = 0
(X+1)+(X+2)+(X+3)+...+(X+100)=5050
=>(X+X+X+...+X)+(1+2+3+...+100)=5050
=>100X+[(1+100)x100:2)]=5050
=>100X+(101x100:2)=5050
=>100X+(10100:2)=5050
=>100X+5050=5050
=>100X=5050-5050
=>100X=0
=>X=0:100
=>X=0
![](https://rs.olm.vn/images/avt/0.png?1311)
(X + 1) + (X + 2) + (X + 3) + … + (X + 99) + (X +100) = 5050
(X+X+X+...+X+X) + (1+100) x 50 = 5050
100 x X + 101 x 50 = 5050
100 x X + 5050 = 5050
100 x X = 5050 - 5050
100 x X = 0
X= 0: 100
X= 0
![](https://rs.olm.vn/images/avt/0.png?1311)
x(x+1) = 2 + 4 + 6 +.....+ 2500
x(x+1) = 1563750 = 1250 . 1251
=> x = 1250
![](https://rs.olm.vn/images/avt/0.png?1311)
x.(x + 1) = 2 + 4 + 6 + ... + 2500
x.(x + 1) = 2.(1 + 2 + 3 + ... + 1250)
x.(x + 1) = 2.(1 + 1250).1250 : 2
x.(x + 1) = 1250.1251
=> x = 1250
Vậy x = 1250
\(x\times\left(x+1\right)=2+4+6+...+2500\)
\(x\times\left(x+1\right)=2\times\left(1+2+3+...+1250\right)\)
\(x\times\left(x+1\right)=2\times\left(1+1250\right)\times1250\div2\)
\(x\times\left(x+1\right)=1250\times1251\)
\(\Rightarrow x=1250\)