\(A=\frac{1.2.3...........99.100}{2.4.6....100}\)

\(=\frac{1.2.3..............99.100}{1.2.2.2.2.3.........50.2}\)

\(=\frac{1.2.3.......50........99.100}{\left(1.2.3........50\right).2.2.....2}\)

\(=\frac{51.52..........99.100}{2.2............2}\)

\(=\frac{51}{2}.\frac{52}{2}...........\frac{100}{2}\)

\(\Rightarrow A=B\)

Ta có : \(1\cdot3\cdot5\cdot...\cdot99=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot99\cdot100}{2\cdot4\cdot6\cdot...\cdot100}\)

\(=\frac{1}{2\cdot1}\cdot\frac{2}{2\cdot2}\cdot...\cdot\frac{100}{2\cdot50}=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot100}{1\cdot2\cdot3\cdot...\cdot50\cdot2\cdot2\cdot2\cdot...\cdot2}\)( 50 thừa số 2 )

\(=\frac{51\cdot51\cdot...\cdot100}{2\cdot2\cdot2\cdot...\cdot2}\)\(=\frac{51}{2}\cdot\frac{52}{2}\cdot\frac{53}{2}\cdot...\cdot\frac{100}{2}\)

Vậy A = B

Chúc bn hok tốt !!! ^_^

bạn lên mạng tra là thấy

 C=1.3.5.7...99 
=>2.4.6...100.C=1.2.3...100 
=>C = (1.2.3....100) / (2.4.6...100)= (1.2.3...50).(51.52...100) / [(2.1)(2.2).(2.3)...(2.50)] 
C=(1.2.3...50).(51.52...100) /[2^50.(1.2.3...50)] =(51.52...100)/2^50 =51/2.52/2.53/2...100/2 =D 
VAy C=D

-->C=\(\frac{1.2.3.4...99.100}{2.4.6....100}\)-->C=\(\frac{1.2.3...99.100}{\left(2.2....2\right)\left(1.2.3.4.5....50\right)}\)[50 chữ số 2]
-->\(C=\frac{51}{2}.\left(\frac{52}{2}\right)....\left(\frac{100}{2}\right)\)=D vậy C=D
________________________________________________________
LI-KE CHO MK NHÉ BN