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\(=\frac{2^3.1.3.5+2^3.3.5.7+2^3.5.7.9+...+2^3.97.99.101}{1.3.5+3.5.7+5.7.9+...+97.99.101}\)
\(=\frac{2^3\left(1.3.5+3.5.7+5.7.9+...+97.99.101\right)}{1.3.5+3.5.7+5.7.9+...+97.99.101}=2^3=8\)
Ta có : \(\frac{3.5.7+9.15.21+12.20.28}{2.4.6+6.12.18+8.16.24}=\frac{3.5.7.\left(1+3.3.3+4.4.4\right)}{2.4.6.\left(1+3.3.3+4.4.4\right)}=\frac{3.5.7}{2.4.6}=\frac{5.7}{2.4.2}=\frac{35}{16}\)
a) \(\frac{3\cdot5\cdot7}{14\cdot55}=\frac{3\cdot5\cdot7}{2\cdot7\cdot11\cdot5}=\frac{3}{2\cdot11}=\frac{3}{22}\)
b) \(\frac{2^7\cdot3^4}{3^6\cdot2^5}=\frac{2^2\cdot2^5\cdot3^4}{3^2\cdot3^4\cdot2^5}=\frac{2^2}{3^2}=\frac{4}{9}\)
c) \(\frac{7\cdot9-7\cdot4}{14\cdot11-14}=\frac{7\left(9-4\right)}{14\cdot\left(11-1\right)}=\frac{7\cdot5}{14\cdot10}=\frac{7\cdot5}{2\cdot7\cdot2\cdot5}=\frac{1}{2\cdot2}=\frac{1}{4}\)
A =2.6.10+6.10.14+10.14.18+...+194.198.202/1.3.5+3.5.7+5.7.9+7.9.11+...+97.99.101
=2.2.2(1.3.5)+2.2.2(3.5.7)+2.2.2(5.7.9)+...+2.2.2(97.99.101)/1.3.5+3.5.7+5.7.9+...+97.99.101
=2.2.2/1
=2^3/1
=8/1
=8
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