So sánh hai phân số  A và  B:

A = 111111/666665

B = 1.2 + 2.4 + 3.6+4.8+5.10 / 3.4+6.8+9.12+12.16+15.20

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

A = \(\frac{1.2.\left(1+2+3+4+5\right)}{3.4.\left(1+2+3+4+5\right)}\)

A = \(\frac{2}{12}=\frac{222222}{1333332}\)

B = \(\frac{111111}{666665}=\frac{222222}{1333330}\)

Vì \(\frac{222222}{1333332}

\(=\frac{14\cdot101+15\cdot101+...+19\cdot101}{20\cdot101+21\cdot101+...+25\cdot101}=\frac{101\cdot\left(14+15+16+17+18+19\right)}{101\cdot\left(20+21+22+23+24+25\right)}\)

\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}=\frac{\left(14+19\right)+\left(15+18\right)+\left(16+17\right)}{\left(20+25\right)+\left(21+24\right)+\left(22+23\right)}=\frac{33.3}{45.3}=\frac{33}{45}=\frac{11}{15}\)

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

A=\(\frac{1.2\left(1+2+3+4+5\right)}{3.4\left(1+2+3+4+5\right)}\)

A=\(\frac{1.2}{3.4}\)

A=\(\frac{1}{6}\)=\(\frac{11111}{66666}\)

Vì\(\frac{11111}{66666}>\frac{11111}{666665}\)

=> A>B

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

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

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

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

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

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

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

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

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

= \(\dfrac{2.55}{4.155}\)

= \(\dfrac{1.55}{2.155}\)

= \(\dfrac{55}{310}=\dfrac{11}{62}\)

= \(\frac{1.2+2.4+3.6+4.8+5.10}{3.2\left(1.2+2.4+3.6+4.8+5.10\right)}=\frac{1}{6}\)
nha :*