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

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

            =\(\frac{1.2+2.2.2+3.3.2+4.4.2+5.5.2}{3.4+3.2.4.2+3.3.4.3+3.4.4.4+3.5.4.5}\)

            =\(\frac{2.\left(4+9+16+25\right)}{3.4.\left(4+9+16+25\right)}\)

            =\(\frac{2}{3.4}=\frac{1}{3.2}=\frac{1}{6}\)

           B=\(\frac{111111}{666666}=\frac{1}{6}\)

=>A=B

l-ike mình nha

\(A=\frac{1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10}{3\cdot2\left(1\cdot2+2\cdot4+3\cdot6+4\cdot8+5\cdot10\right)}=\frac{1}{6}\)

\(B=\frac{111111}{666666}=\frac{1\cdot111111}{6\cdot111111}=\frac{1}{6}\)

Vì 1/6 =1/6 nên A=B

A=B

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

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

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

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

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

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

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

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

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

= \(\dfrac{2.55}{4.155}\)

= \(\dfrac{1.55}{2.155}\)

= \(\dfrac{55}{310}=\dfrac{11}{62}\)

Lục Minh Hoàng cho mình hỏi tại sao lại có 1/2 vậy ?

1/3+1/15+1/35+1/63+1/99+1/143+1/195

=1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15

suy ra 2(1/1*3+1/3*5+1/5*7+1/7*9+1/9*11+1/11*13+1/13*15)

=2/1*3+2/3*5+2/5*7+2/7*9+2/9*11+2/11*13+2/13*15

=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15

=1-1/15

=14/15

a=14/15 chia 2=7/15

ảnh có dễ thươg các bạn!