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用数学归纳法证明1+n/2≤1+1/2+1/3+...+1/(2^n)≤1/2+n当n=k+1时,1+1/2+1/3+...+1/2^k+1/(2^k+1)+...+1/2^(k+1)>=1+k/2+1/(2^k+1)+...+1/2^(k+1)>1+k/2+1/2^(k+1)+...+1/2^(k+1)>1+k/2+[2^(k+1)-2^k]/2^(k+1)=1+(k+1)/21+1/2+1/3+...+1/2^k+1/(2^k+1)+...+1/2^(k+1)

分类: 作业答案 • 2022-08-02 12:20:21
问题描述：

用数学归纳法证明1+n/2≤1+1/2+1/3+...+1/(2^n)≤1/2+n
当n=k+1时,
1+1/2+1/3+...+1/2^k+1/(2^k+1)+...+1/2^(k+1)
>=1+k/2+1/(2^k+1)+...+1/2^(k+1)
>1+k/2+1/2^(k+1)+...+1/2^(k+1)
>1+k/2+[2^(k+1)-2^k]/2^(k+1)=1+(k+1)/2
1+1/2+1/3+...+1/2^k+1/(2^k+1)+...+1/2^(k+1)

答

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