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

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

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

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

a) 4000 x 2 

Nhẩm: 4 nghìn x 2 = 8 nghìn

            4000 x 2 = 8000

b) 3000 x 3

     Nhẩm: 3 nghìn x 3 = 9 nghìn

                3000 x 3 = 9000

c) 2000 x 4 

   Nhẩm: 2 nghìn x 4 = 8 nghìn

              2000 x 4 = 8000

a) x.(x+1) = (2+2500)[(2500-2):2+1]:2 =2502.625=1563750

  x(x+1) = 1250(1250+1) 

=> x = 1250

b) 1+2+3+4+.......+x = 820

 (1+x)x:2 =820

x(x+1) = 1640 =40(40+1)

=> x = 40

 X x ( X - 13 ) = 0

=> XxX-Xx13=0

=> XxX-13X=0

=XxX=13X

=>X=12X

=> x=0

b) ( X - 1) x ( 3 x X - 15 ) = 0

=> \(\orbr{\begin{cases}x-1=0\\3x-15=0\end{cases}}\)giải ra 

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

Dãy  2 + 4 + 6 + ... +2500 có số số hạng là:

(2500-2):2+1=1250 (số)

Tỗng của dãy là:

(2500+2)x1250:2=1563750

=> X x ( X + 1 )=1563750

Giải ra 

xong nhé

a) X x ( X - 13 ) = 0

\(\hept{\begin{cases}x=0\\x-13=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x=13\end{cases}}}\)

vậy..................

b) ( X - 1) x ( 3 x X - 15 ) = 0

\(\hept{\begin{cases}x-1=0\\3\cdot x-15=0\end{cases}\Rightarrow\hept{\begin{cases}x=1\\3x=15\end{cases}}}\Rightarrow\hept{\begin{cases}x=1\\x=5\end{cases}}\)

vậy x=1

x=5

bài 1: tính hợp lý

a) 16+273+84+27

= (273 + 27) + (16 + 84)

= 300 + 100 = 400

b)2,5x11+2,5x89

= 2,5 x ( 11 + 89)

= 2,5 x 100 = 250

c)12x25+2x27x6+3x48x4

= 12x25 + 12x27 +12x48

= 12 x (25+27+48)

=12 x 100

=1200

vẫn còn các bài khác mà 

bạn làm đi rồi mik cho

3. \(\left(\frac{1}{2^5}\right)^{25}=\left(\frac{1^5}{2^5}\right)^{25}=\left[\left(\frac{1}{2}\right)^5\right]^{25}=\left(\frac{1}{2}\right)^{125}\)

\(\left(\frac{1}{3^{25}}\right)^5=\left(\frac{1^{25}}{3^{25}}\right)^5=\left[\left(\frac{1}{3}\right)^{25}\right]^5=\left(\frac{1}{3}\right)^{125}\)

Vì \(\frac{1}{2}>\frac{1}{3}\Rightarrow\left(\frac{1}{2^5}\right)^{25}>\left(\frac{1}{3^{25}}\right)^5\)

1. \(3^{800}=\left(3^8\right)^{100}=6561^{100}\)

\(5^{500}=\left(5^5\right)^{100}=3125^{100}\)

Vì \(6561>3125\Rightarrow3^{800}>5^{500}\)

2. \(\left(-2\right)^{3000}=\left[\left(-2\right)^3\right]^{1000}=\left(-8\right)^{1000}\)

\(\left(-3\right)^{2000}=\left[\left(-3\right)^2\right]^{1000}=9^{1000}\)

Vì \(-8< 9\Rightarrow\left(-2\right)^{3000}< \left(-3\right)^{2000}\)