当n属于N*,求证:1⼀2<=1⼀(n+1)+1⼀(n+2)+......+1⼀2n<1

2025-02-23 22:58:54
推荐回答(1个)
回答1:

左边:1/(n+1)+1/(n+2)+......+1/2n≥1/2n+1/2n+......+1/2n=n/2n=1/2
右边:1/(n+1)+1/(n+2)+......+1/2n≤1/(n+1)+1/(n+1)+....1/(n+1)=n/(n+1)<1

(左边就是把分母都换成2n,缩小,而右边是把分母换成n+1,放大,这就是所谓的放缩法)