Question

Докажите, что $frac{1}{2} * frac{3}{4} * frac{5}{6} * ... frac{9999}{10000} < 0,01$

Answer 1

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