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

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

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

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

ket qua la 125

k mik nha bn

2500 x 5 : 100= 

=12500 : 100

=125

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

= (2+2500) x 625

= 2502 x 625 = 1563750 =  1250 x 1251

Vậy x=1250

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

1m3=100dm3

nhầm, 1m3=1000dm3

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