L=(1x2+2x1x2x2+3x1x2x3+4x1x2x4+5x1x2x5)/(3x4+2x3x4x2+3x3x4x3+4x3x4x4+5x3x4x5)

L=(1+2x2+3x3+4x4+5x5)(1x2)/(1+2x2+3x3+4x4+5x5)(3x4)

L=(1x2)/(3x2x2)

L=1/6

a) Ta có \(\frac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

= \(\frac{1.2+1.2.2.2+1.3.2.3+1.4.2.4+1.5.2.5}{3.4+3.2.4.2+3.3.4.3+3.4.4.4+3.5.4.5}\)

= \(\frac{1.2+1.2.4+1.2.9+1.2.16+1.2.25}{3.4+3.4.4+3.4.9+3.4.16+3.4.25}\)

= \(\frac{1.2.\left(1+4+9+16+25\right)}{3.4.\left(1+4+9+16+25\right)}\)

= \(\frac{1.2.55}{3.4.55}\)

= \(\frac{1.2.55}{3.2.2.55}\)

= \(\frac{1}{3.2}\)

= \(\frac{1}{6}\)

b) \(\frac{111111}{666665}=\frac{111111}{666665}\)

(dấu "." là dấu "x")

mk làm tiếp 

Ta có : \(\frac{1}{6}=\frac{111111}{666666}\)

Vì \(\frac{111111}{666666}< \frac{111111}{666665}\)

=> \(\frac{1}{6}< \frac{111111}{666665}\)

So sánh A và B biết
B= (1.2+2.4+3.6+4.8+5.10) / (3.4+6.8+9.12+12.16+15.20)
A=111111/666665
ta có:
Tử B=1.2+2.4+3.6+4.8+5.10
=2+8+18+48+50=126
Mẫu B=3.4+6.8+9.12+12.16+15.20
=12+48+108+192+300=660
Phân số 126/660
So sánh phân sô126/660 và phân số 111111/666665
hay so sánh 126.666665 và 111111.660
hay 83999790 và 73333260
vậy 83999790>73333260
nên phân số B>A

\(\text{1x2 + 2x4 + 3x6 + 4x8 + 5x10 / 3x4 + 6x8 + 9x12 + 12x16 + 15x20}\)

\(\text{Mẫu số : 3x4 + 6x8 + 9x12 + 12x16 + 15x20 = 3 x 2 x (1x2 + 2x4 + 3x6 + 4x8 + 5x10)}\)

\(\text{Vậy (1x2 + 2x4 + 3x6 + 4x8 + 5x10) / (3 x 2 x (1x2 + 2x4 + 3x6 + 4x8 + 5x10)) = 1/3x2 = 1/6}\)

\(A=\frac{111111}{666665}=\)bạn tự rút gọn nha !

1x2 + 2x4 + 3x6 + 4x8 + 5x10 / 3x4 + 6x8 + 9x12 + 12x16 + 15x20

Mẫu số : 3x4 + 6x8 + 9x12 + 12x16 + 15x20 = 3 x 2 x (1x2 + 2x4 + 3x6 + 4x8 + 5x10)

Vậy (1x2 + 2x4 + 3x6 + 4x8 + 5x10) / (3 x 2 x (1x2 + 2x4 + 3x6 + 4x8 + 5x10)) = 1/3x2 = 1/6

=> A ... B

3x4x5 =60                                 6x8+12x16=240

10x2x6  =120                               4x12x6x8 =2304         

\(\dfrac{3.4.5}{10.2.6}=\)\(\dfrac{3.2.2.5}{2.5.3.2}=\dfrac{1}{0}\)

=> hình như đề sai phải k pạn?

Vì k có phép chia 1:0 nên k có phân số 1/0

còn phân số thứ 2 mk xin rút lui

N = 1/1x5 + 1/5x10 + 1/10x15 + 1/15x20 + .....+1/2005 x 2010

N = 1 - 1/5 +1/5-1/5+1/10-1/15+1/5-1/20+.....+1/2005-1/2010

N = 1 - 1/2010

N = 2009/2010

Ta có:

\(N=\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\)

\(\Rightarrow Nx5=\left(\frac{1}{1x5}+\frac{1}{5x10}+\frac{1}{10x15}...+\frac{1}{2005x2010}\right)x5\)

\(=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}...+\frac{5}{2005x2010}\)

\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)

\(=1-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)

\(\Rightarrow N=\frac{2009}{2010}:5=\frac{2009}{2010}x\frac{1}{5}=\frac{2009}{10050}\)

Bạn thuỳ dung ơi cho hỏi sao 5/(1x5) = 1 - 1/5 vậy ???

(5/5x10+5/10x15+5/15x20+...+5/95x100)

=  (1/5-1/10+1/10-1/15+1/15-1/20+....+1/95-1/100):5

=(1/5-1/100):5

=19/500

\(\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+......+\frac{1}{2005.2010}\)

\(=\frac{1}{5}+\frac{1}{5}\left(\frac{5}{5.10}+\frac{5}{10.15}+\frac{5}{15.20}+.......+\frac{5}{2005.2010}\right)\)

\(=\frac{1}{5}+\frac{1}{5}\left(\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+......+\frac{1}{2005}-\frac{1}{2010}\right)\)

\(=\frac{1}{5}+\frac{1}{5}\left(\frac{1}{5}-\frac{1}{2010}\right)\)

\(=\frac{1}{5}+\frac{1}{5}\frac{401}{2010}\)

\(=\frac{1}{5}+\frac{401}{10050}=\frac{2411}{10050}\)

N = (1/1 - 1/5 + 1/5 -1/10 + ... + 1/2005 - 1/2010 ) x 5

N = (1/1 - 1/2010 ) x5

N = 2009/2010 x5

N = 2009/402

(N-1/5)x5 = 5/5x10 + 5/10x15 + ......... + 5/2005x2010 = 1/5 - 1/10 + 1/10 - 1/15 + 1/15 -.... - 1/2005 + 1/2005 - 1/2010

= 1/5 - 1/2010 = 401/2010

<=>N-1/5 = 401/10050      <=> N = 401/10050 + 1/5 

=> N = 2411 / 10050

\(N=\frac{1}{1x5}+\frac{1}{5x10}+...+\frac{1}{2005x2010}\)

\(\Rightarrow5N=\frac{5}{1x5}+\frac{5}{5x10}+\frac{5}{10x15}+...+\frac{5}{2005x2010}\)

\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+...+\frac{1}{2005}-\frac{1}{2010}\)

\(\Rightarrow5N=1-\frac{1}{5}-\frac{1}{2010}\)

\(\Rightarrow5N=\frac{4}{5}-\frac{1}{2010}\)

\(\Rightarrow5N=\frac{1607}{2010}\)

\(\Rightarrow N=\frac{1607}{10050}\)

Nhấn đúng cho mk nha!!!!!!!!!

\(=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+..........+\frac{1}{2005}-\frac{1}{2010}\)

\(=\frac{1}{1}-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)