Thôi không cần nữa giải ra rồi

4896 phải không?

Sai rồi phải bằng 1 mới đúng

giải ra hết hộ mình nhé!

\(A=\frac{1X2X3+2X4X6+4X8X12+8X16X24}{2X3X4+4X6X8+8X12X16+8X24X32}\)

\(A=\frac{1+1+1+1}{4+4+4+2}\)

\(A=\frac{4}{14}\)

CHÚC BẠN HỌC GIỎI !

ai k cho mình tròn 70 với

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

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

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

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

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

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

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