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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) \(\frac{12\cdot13+24\cdot26+36\cdot39}{24\cdot26+48\cdot52+72\cdot78}\)
\(=\frac{12\cdot13\cdot\left(1+2\cdot2+3\cdot3\right)}{24\cdot26\cdot\left(1+2\cdot2+3\cdot3\right)}\)
\(=\frac{12\cdot13}{24\cdot26}=\frac{1}{4}\)
\(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\frac{2\cdot3\cdot\left(1+2\cdot2+7\cdot7\right)}{3\cdot5\cdot\left(1+2\cdot2+7\cdot7\right)}=\frac{2\cdot3}{3\cdot5}=\frac{2}{5}\)
\(\frac{1.2+2.4+3.6+4.8+5.10}{3.4+6.8+9.12+12.16+15.20}\)
\(=\frac{1.2+2.2.2+3.3.2+4.4.2+5.5.2}{3.4+2.3.2.4+3.3.3.4+4.3.4.4+5.3.5.4}\)
\(=\frac{2.\left(1+2.2+3.3+4.4+5.5\right)}{3.4.\left(1+2.2+3.3+4.4+5.5\right)}\)
\(=\frac{1}{6}\)
= \(\frac{1.2+2.4+3.6+4.8+5.10}{3.2\left(1.2+2.4+3.6+4.8+5.10\right)}=\frac{1}{6}\)
nha :*
