2+4+6+8+10+.........+2500 = 1563750 .

x.( x+1 ) = 1250.1251

Vậy x = 1250 .

x(x+1)=1563750

vì x và x+1 là 2 số liên tiếp

x=1250

tick đúng nha

a:Sửa đề: 1x3+2x4+...+99x101

\(=1\times\left(1+2\right)+2\times\left(2+2\right)+\cdots+99\times\left(99+2\right)\)

\(=\left(1\times1+2\times2+\cdots+99\times99\right)+2\times\left(1+2+\cdots+99\right)\)

\(=\frac{99\times\left(99+1\right)\times\left(2\times99+1\right)}{6}+2\times\frac{99\times100}{2}\)

\(=\frac{99\times100\times199}{6}+99\times100=33\times50\times199+99\times100\)

\(=33\times50\times\left(199+3\times2\right)=33\times50\times205=338250\)

b: \(\frac89\times\frac{15}{16}\times\ldots\times\frac{2499}{2500}\)

\(=\left(1-\frac19\right)\times\left(1-\frac{1}{16}\right)\times\ldots\times\left(1-\frac{1}{2500}\right)\)

\(=\left(1-\frac13\right)\times\left(1-\frac14\right)\times\ldots\times\left(1-\frac{1}{50}\right)\times\left(1+\frac13\right)\times\left(1+\frac14\right)\times\ldots\times\left(1+\frac{1}{50}\right)\)

\(=\frac23\times\frac34\times\ldots\times\frac{49}{50}\times\frac43\times\frac54\times\ldots\times\frac{51}{50}=\frac{2}{50}\times\frac{51}{3}=\frac{17}{25}\)

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 

\(x\times\left(x+1\right)=2+4+6+...+2500\)
\(x\times\left(x+1\right)=2\times\left(1+2+3+...+1250\right)\)
\(x\times\left(x+1\right)=2\times\left(1+1250\right)\times1250\div2\)
\(x\times\left(x+1\right)=1250\times1251\)
\(\Rightarrow x=1250\)
 

x(x+1) = 2 + 4 + 6 +.....+ 2500

x(x+1) = 1563750 = 1250 . 1251

=> x = 1250

a)123-5*(x+4)=38

5 ( x + 4 ) = 123 - 38

5 ( x + 4) =  85

x + 4 = 85 : 5

x + 4 =17

x = 17 - 4

x = 13

X×(1+1)+(x×2+4)+x×(3+7)+...+(x×11+28)=239

X×(1+1)=2+4+6+...+2500

Xx2=1563750

x=1563750:2

x=781875

Barbie

x * ( x + 1 ) = 2 + 4 + 6 + ... + 2500

Số số hạng:

( 2500 - 2 ) : 2 + 1 = 1250 ( số hạng)

=> 2 + 4 + 6 + 8 + 10 + 2500

= (  2500+ 2 ) * 1250 : 2 

= 1563750

Ta có: x * ( x + 1 ) = 1563750

           Màk 1563750 = 1250 * 1251

                  =>      x    = 1250

Ps : Mk ko chắc lắm! 

^^ Chúc bạn học tốt nha!!!  

x*(x+1)=2+4+6+...+2500
x*x+x=1563750
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