Xét tử: 2.4+4.8+8.12+12.16+16.20 = 2.1.2.2 + 2.2.2.4 + 2.2.4.6 + 2.2.6.8 + 2.2.8.10

                                                   = 2.2.(1.2+2.4+4.6+6.8+8.10)

=> 2.4+4.8+8.12+12.16+16.20/1.2+2.4+4.6+6.8+8.10 = 2.2.(1.2+2.4+4.6+6.8+8.10) / 1.2+2.4+4.6+6.8+8.10

                                                                               = 2.2 = 4

camon nhan (:

4.

tử của A= 4(1.2 + 2.4+...+8.10) 

mẫu của A= 1.2 + 2.4+...+8.10 nên A=4

a)
\(\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot4+6\cdot8+9\cdot12+12\cdot16+15\cdot20}\)

\(=\frac{1\cdot2\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}{3\cdot4\cdot\left(1+2\cdot2+3\cdot3+4\cdot4+5\cdot5\right)}\)

\(=\frac{1\cdot2}{3\cdot4}=\frac{1}{6}\)

b) \(\frac{12\cdot13+24\cdot26+36\cdot39}{24\cdot26+48\cdot52+72\cdot78}\)

\(=\frac{12\cdot13\cdot\left(1+2\cdot2+3\cdot3\right)}{24\cdot26\cdot\left(1+2\cdot2+3\cdot3\right)}\)

\(=\frac{12\cdot13}{24\cdot26}=\frac{1}{4}\)

\(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3\cdot\left(1+2\cdot2+7\cdot7\right)}{3\cdot5\cdot\left(1+2\cdot2+7\cdot7\right)}=\frac{2\cdot3}{3\cdot5}=\frac{2}{5}\)

\(=\frac{1.2\left(1+2.2+3.3+4.4+5.5\right)}{3.4\left(1+2.2+3.3+4.4+5.5\right)}\)

\(=\frac{1.2}{3.4}=\frac{1}{6}\)

\(\frac{1.2+2.4+3.6+4.8+5.10}{3.2.2+2.3.4.2+3.3.6.2+4.3.8.2+5.3.10.2}\)=\(\frac{1}{3.2+3.2+3.2+3.2+3.2}\)=\(\frac{1}{30}\)

vậy bt trên =\(\frac{1}{30}\)

tk nhé

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(=\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+3.4.2.2+3.4.3.3+3.4.2.8+3.4.5.5}\)

\(=\dfrac{1.2.\left(4+3^2+2.8+5^2\right)}{3.4.\left(4+3^2+2.8+5^2\right)}\)

\(=\dfrac{1}{6}\)

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

\(=\dfrac{1.2+1.2.2^2+1.2.3^2+1.2.4^2+1.2.5^2}{3.4+3.4.2^2+3.4.3^2+3.4.4^2+3.4.5^2}\)

\(=\dfrac{1.2\left(1+2^2+3^2+4^2+5^2\right)}{3.4\left(1+2^2+3^2+4^2+5^2\right)}\\ =\dfrac{2}{12}=\dfrac{1}{6}\)

\(\dfrac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)

= \(\dfrac{2\left(1+4+9+16+25\right)}{4\left(3+12+27+48+65\right)}\)

= \(\dfrac{2.55}{4.155}\)

= \(\dfrac{1.55}{2.155}\)

= \(\dfrac{55}{310}=\dfrac{11}{62}\)