利用放缩法证明1⼀(n+1)+1⼀(n+2)+1⼀(n+3)+......+1⼀(2n+1)<4⼀5

2024-11-29 15:52:13
推荐回答(2个)
回答1:

放缩法证明方法:

回答2:

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)