\(M=\frac{1.2.4+2.4.8+4.8.16+8.16.32}{1.3.4+2.6.8+4.12.16+8.24.32}\)

\(M=\frac{\left(1.2.4\right).1^3+\left(1.2.4\right).2^3+\left(1.2.4\right).4^3+\left(1.2.4\right).8^3}{\left(1.3.4\right).1^3+\left(1.3.4\right).2^3+\left(1.3.4\right).4^3+\left(1.3.4\right).8^3}\)

\(M=\frac{\left(1.2.4\right).\left(1^3+2^3+4^3+8^3\right)}{\left(1.3.4\right).\left(1^3+2^3+4^3+8^3\right)}\)

M = \(\frac{2}{3}\)

\(\frac{2.4+2.4.8+4.8.16+8.16.32}{3.4+2.6.8+4.12.16+8.16.32}\)

\(=\frac{2.\left(4+2.2.8+4.4.16+8.8.32\right)}{3.\left(4+2.2.8+4.4.16+8.8.32\right)}\)

\(=\frac{2}{3}\)

cảm ơn bạn

\(=\frac{1.2.4\left(1+2.2.2+4.4.4+8.8.8+16.16.16\right)}{1.3.4\left(1+2.2.2+4.4.4+8.8.8+16.16.16\right)}=\frac{2}{3}\)

\(\frac{1.2.4+2.4.8+4.8.16+...+128.256.512}{1.3.4+2.6.8+4.12.16+...+128.384.512}\)

\(=\frac{1.2.4.\left(1^3+2^3+4^3+8^3...+128^3\right)}{1.3.4.\left(1^3+2^3+4^3+8^3...+128^3\right)}\)

\(=\frac{2}{3}\)

Vì 2/3 = 8/12 < 9/12 = 3/4

\(\Rightarrow\frac{1.2.4+2.4.8+4.8.16+...+128.256.512}{1.3.4+2.6.8+4.12.16+...+128.384.512}< \frac{3}{4}\)

\(=\frac{2\left(4+2.2.8+4.4.16+8.8.32\right)}{3\left(4+2.2.8+4.4.16+8.8.32\right)}=\frac{2}{3}\)

thế thì có nhiều chi tiết bạn có thể giải hộ mình đc ko ?