已知n是正整数，求证1/(n+1) + 1/(n+2) + ......+1/2n < 25/36这是加试第二题（一共3题）。

原式=1-1/2+1/3-1/4+1/5-1/6+1/7-1/8……+1/（2N+1）-1/（2N+2) =1-1/2+1/3-1/4+1/5-1/6+1/7-1/8……+1/13-1/14+(1/15-1/16)+……+(1/（2N+1）-1/（2N+2)) <1-1/2+1/3-1/4+1/5-1/6+1/7-1/8……+1/13-1/14+(1/14-1/16)+(1/16-1/18)+……+)+……+(1/2N-1/（2N+2)) =1-1/2+1/3-1/4+1/5-1/6+1/7-1/8……+1/13-1/14+1/2(1/14-1/2n+2） <1-1/2+1/3-1/4+1/5-1/6+1/7-1/8……+1/13-1/14+1/28 =250241/360360<25/36

这不就是何佩佩的方法?有没有别的?