4/5×6/7×8/9×10/11×12/13×14/15.×1000000/1000001与0.002比较大小

Question

4/5×6/7×8/9×10/11×12/13×14/15.×1000000/1000001
与0.002比较大小

Answer 1

设A=4/5×6/7×8/9×10/11×12/13×14/15……×1000000/1000001
则A=(4×6×8×10×……×1000000)/(5×7×9×11×……×1000001)
B=0.002
B/A=1000001!/{500×6×(500000!)^2}
=500001×500002×500003×……×1000001/(500×6×500000!)
=500001×500002×500003×……×1000001/3000×2×3×4×……×500000
很明显B/A>1,则B>A,即
0.002>4/5×6/7×8/9×10/11×12/13×14/15×……×1000000/1000001