A=(1/2)*(3/4)*(5/6)*...*(99/100)
假设C=(2/3)*(4/5)*(6/7)*...*98/99*(100/101)
则C>A
A*C=1/101,1/101<1/100=1/10*1/10
A*C<1/10*1/10
∵C>A
∴A<1/10
即A<B
A=(1/2)*(3/4)*(5/6)*...*(99/100)
假设C=(2/3)*(4/5)*(6/7)*...*98/99*(100/101)
则C>A
A*C=1/101,1/101<1/100=1/10*1/10
A*C<1/10*1/10
∵C>A
∴A<1/10
即A<B