Докажите, что [latex] \frac{1}{2} * \frac{3}{4} * \frac{5}{6} * ... \frac{9999}{10000} меньше 0,01[/latex]

[latex]\frac{1}{2}*\frac{3}{4}*\frac{5}{6} *...\frac{9999}{10000}<0.01\\ \frac{1*3*5*7*9*11*13...*9999}{(2*1)*(2*2)*(2*3)*(2*4)*(2*5)...(2*5000)}<0.01\\ \frac{1*3*5*7*9*11*13...*9999}{2^{5000}*1*2*3*4*5*6*7*...5000}<0.01\\ \frac{1}{2^{7500}*1*2*3*4*5*6*...2500}<0.01\\ \frac{1}{2^{7500}}<0.01\\ verno[/latex]