Question

二分之一乘四分之三乘六分之五乘八分之七……一直乘到一百分之九十九的积和十分之一比大小

急

Answer 1

解:由于
1/2×3/4×5/6×7/8…×99/100
<2/3×4/5×6/7×8/9…×100/101 ···········①
所以：
(1/2×3/4×5/6×7/8…×99/100)^2
<(1/2×3/4×5/6×7/8…×99/100)×(2/3×4/5×6/7×8/9…×100/101)
=1/2×2/3×3/4×4/5×5/6×6/7×...×99/100×100/101
=1/101<1/100
直接开方，得：
1/2×3/4×5/6×7/8……×99/100<1/10