用放缩法证明:1+1⼀2+1⼀3+1⼀4+...+1⼀2 ^n≤n

2024-12-14 20:04:05
推荐回答(1个)
回答1:

1/2+1/3≤(1/2)*2=1
1/4+...+1/7<=1/4*4=1
1/8+...+1/15<=1/8*8=1
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1+1/2+1/3+1/4+...+1/2 ^n≤1+1/2*2+1/4*4+^^^^^^+1/2^(n-1)*2^(n-1)=n
(本题应该是1+1/2+1/3+1/4+...+1/(2 ^n-1)≤n ,否则n=1时1+1/2^1不小于等于1,本题出错!)