1除以3×5+1除以5×7+1除以7×9+1除以9×11+.1除以99×101

1÷(3×5)=(1/2)×(5-3)÷(3×5)=(1/2)×[5÷(3×5)-3÷(3×5)]=(1/2)×(1/3-1/5)同理1÷(5×7)=(1/2)×(7-5)÷(5×7)=(1/2)×[7÷(5×7)-5÷(5×7)]=(1/2)×(1/5-1/7)后面以此类推所以原式=(1/2)×(1-3-1/5+1/5-1/7...