放缩法证明方法:
n=1时1/3+1/2=5/6明显不成立n=2时1/3+1/4+1/5=47/60<48/60成立当n>3时有设An=1/(n+1)+1/(n+2)+1/(n+3)+......+1/(2n+1)所以An+1=1/(n+2)+1/(n+3)+......+1/(2n+1)+1/(2n+2)+1/(2n+3)An-An+1=1/(n+1)-1/(2n+2)+1/(2n+3)>0所以1/(n+1)+1/(n+2)+1/(n+3)+......+1/(2n+1)