Ta có : 1.3.5.7. ... .59

       = \(\frac{1.2.3.4.5.....58.59.60}{2.4.6.8.....58.60}\) 

       = \(\frac{\left(1.2.3.....30\right).\left(31.32.....60\right)}{\left(1.2.3.....30\right).2.2.....2}\)

       = \(\frac{31.32.....60}{2.2.....2}\)

       = \(\frac{31}{2}.\frac{32}{2}.....\frac{58}{2}.\frac{60}{2}\) ( đpcm )

\(1.3.5.7.....59=\frac{1.2.3.4.....60}{2.4.6.....60}=\frac{\left(1.2.3.....30\right).\left(31.32.....60\right)}{\left(1.2\right).\left(2.2\right).\left(3.2\right).....\left(30.2\right)}\)

\(=\frac{\left(1.2.3.....30\right).\left(31.32.....60\right)}{\left(1.2.3.....30\right).\left(2.2.....2\right)}=\frac{31}{2}.\frac{32}{2}.....\frac{60}{2}\)

a: \(M=\frac{53\cdot71-18}{71\cdot52+53}\)

\(=\frac{71\cdot52+71-18}{71\cdot52+53}=\frac{71\cdot52+53}{71\cdot52+53}=1\)

\(N=\frac{54\cdot107-53}{53\cdot107+54}\)

\(=\frac{53\cdot107+107-53}{53\cdot107+54}=\frac{53\cdot107+54}{53\cdot107+54}\)

=1

=>M=N

b: \(A=\frac{7\cdot9+14\cdot27+21\cdot36}{21\cdot27+42\cdot81+63\cdot108}\)

\(=\frac{7\cdot9\cdot\left(1+2\cdot3+3\cdot4\right)}{21\cdot27\cdot\left(1+2\cdot3+3\cdot4\right)}=\frac{7}{21}\cdot\frac{9}{27}=\frac13\cdot\frac13=\frac19\)

\(B=\frac{37}{333}=\frac{37}{37\cdot9}=\frac19\)

Do đó: A=B

Q = 1.3.5.7...59 = \(\frac{\left(2.4.6...60\right).\left(1.3.5.7...59\right)}{\left(2.4.6...60\right)}=\frac{1.2.3.4...59.60}{2^{30}.\left(1.2.3...30\right)}=\frac{31.32.33...60}{2^{30}}=\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}\)= P

Mình không hiểu, trần thị Loan làm như nào đấy giải thích rõ hơn

P=Q

Chúc bạn một kì nghỉ thú vị nhé !

\(P=\frac{31}{2}.\frac{32}{2}.\frac{33}{2}......\frac{60}{2}=\frac{31.32.33.......60}{2.2.2........2}\)

Từ 31-60 có:60-31+1=30 (số hạng)

=>ở mẫu có 30 số hạng 2

=>\(P=\frac{32.32.33......60}{2^{30}}=\frac{\left(31.32.33.....60\right).\left(1.2.3.........30\right)}{2^{30}.\left(1.2.3.......30\right)}\)

\(P=\frac{\left(1.3.5.....59\right).\left(2.4.6......60\right)}{\left(2.4.6......60\right)}=1.3.5.....59=Q\)

=>P=Q

Ta có:

31/2.32/2.33/2....60/2=31.32......60/2^30

=(31.32.33....60)(1.2.3....30)/2^30(1.2.3...30)

=(1.3.5...59)(2.4.6...60)/(2.4.6...60)=1.3.5...59

=>P=Q

nhớ ****

cái dòng 3, 4 mk ko hiểu sao 2^30.(1.2.3....30) lại bằng 2.4.6...60