\(\frac{3.4.5}{10.2.6}=\frac{3.2.2.5}{2.5.2.2.3}=\frac{1}{2}\)

\(\frac{6.8.12.16}{4.12.6.8}=\frac{6.8.12.4.4}{4.12.6.8}=\frac{4}{1}=4\)

a)=1/2

b) =4

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

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

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

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

\(=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+...+\dfrac{1}{18\cdot19}-\dfrac{1}{19\cdot20}\)

=1/2-1/380

=190/380-1/380

=189/380

Gọi biểu thức trên là S. Ta có :

\(S=\dfrac{1}{1\times2\times3}+\dfrac{1}{2\times3\times4}+\dfrac{1}{3\times4\times5}+...+\dfrac{1}{18\times19\times20}\)

\(=\dfrac{1}{2}\times\left(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{18\times19\times20}\right)\)

Trước tiên, ta áp dụng : \(\dfrac{2}{a\left(a+1\right)\left(a+2\right)}=\dfrac{1}{a\left(a+1\right)}-\dfrac{1}{\left(a+1\right)\left(a+2\right)}\)

Ta sẽ có : 

\(S=\dfrac{1}{2}\times\left(\dfrac{1}{1\times2}-\dfrac{1}{2\times3}+\dfrac{1}{2\times3}-\dfrac{1}{3\times4}+\dfrac{1}{3\times4}-\dfrac{1}{4\times5}+...+\dfrac{1}{18\times19}-\dfrac{1}{19\times20}\right)\)

\(=\dfrac{1}{2}\times\left(\dfrac{1}{1\times2}-\dfrac{1}{19\times20}\right)\)

\(=\dfrac{1}{2}\times\dfrac{1}{1\times2}-\dfrac{1}{2}\times\dfrac{1}{19\times20}\)

\(=\dfrac{1}{4}-\dfrac{1}{760}=\dfrac{189}{760}\)

`=1/2(1/1×2 - 1/2×3 + 1/2×3 - 1/3×4 + 1/3×4 - 1/4×5 + ... + 1/18×19 - 1/19×20)`
`=1/2(1/2 - 1/19×20)`
`=1/2×189/380 `
`=189/760`

\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{6.7.8}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{6.7}-\frac{1}{7.8}\)

\(=\frac{1}{1.2}-\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{56}\)

\(=\frac{28}{56}-\frac{1}{56}=\frac{27}{56}\)

Dấu . là nhân nha

\(\frac{2}{1.2.3}=\frac{1}{1.2}-\frac{1}{2.3}\)

\(\frac{2}{2.3.4}=\frac{1}{2.3}-\frac{1}{3.4}\)

.......................................

\(\frac{2}{6.7.8}=\frac{1}{6.7}-\frac{1}{7.8}\)

S= \(\frac{1}{1.2}-\frac{1}{7.8}=\frac{27}{56}\)

\(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{6.7.8}\)

\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{6.7}-\frac{1}{7.8}\)

\(=\frac{1}{1.2}-\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{56}\)

\(=\frac{28}{56}-\frac{1}{56}=\frac{27}{56}\)