Question

1/1*3+1/3*5+1/5*7+1/7*9+.....1/99*101 等于多少？

速度给答案

Answer 1

1/3+1/3×5＋1/5×7+1/7×9+…＋或旦1/97×99＋1/99×101

=1/银渗2[1-1/3]+1/2[1/3-1/5]+...+1/2[1/99-1/101]

=1/2[1-1/3+1/3-1/锋团脊5+....+1/99-1/101]

=1/2[1-1/101]

=1/2*100/101

=50/101

Answer 2

1/1*3+1/3*5+1/5*7+1/游袭7*9……乎迅+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/岁磨此5=（5-3）/3*5=2/3*5
……
所以要除以2。