1/3+1/3×5+1/5×7+1/7×9+…+1/97×99+1/99×101
=1/2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]
=1/2[1-1/3+1/3-1/5+....+1/99-1/101]
=1/2[1-1/101]
=1/2*100/101
=50/101
1/1*3+1/3*5+1/5*7+1/7*9……+1/99*101
=(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9……+1/99-1/101)/2
=(1-1/101)/2
=50/101
1-1/3=(3-1)/1*3=2/1*3
1/3-1/5=(5-3)/3*5=2/3*5
……
所以要除以2。