利用放缩法证明1/(n+1)+1/(n+2)+1/(n+3)+.+1/(2n+1)<4/5

问题描述:

利用放缩法证明1/(n+1)+1/(n+2)+1/(n+3)+.+1/(2n+1)<4/5

n=1时1/3+1/2=5/6明显不成立n=2时1/3+1/4+1/5=47/603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)...