求1/100+1/101+1/102+.+1/300的整数部分

1/100 + 1/101 + ...+ 1/300
< 1/100 * 100 + 1/200 * 101
< 1 + 0.6 < 2
1/100 + 1/101 + ...+ 1/300
= 1/100 + (1/101 + ...1/125) + (1/126 + ...+ 1/150) + (1/151 + ...+ 1/175) + (1/176 + ...+ 1/200) + (1/201 + ...+ 1/225) + (1/226 + ...+ 1/250) + (1/251 + ...+ 1/275) + (1/275 + ...+ 1/300)
> 1/100 + 1/125 * 25 + 1/150 * 25 + 1/175 * 25 + 1/200 * 25 + 1/225 + 25 + 1/250 * 25 + 1/275 * 25 + 1/300 * 25
= 1/100 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 = 1.0297 > 1