用数学归纳法证明:当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24

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用数学归纳法证明:当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24

用数学归纳法证明:当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24
用数学归纳法证明:当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24

用数学归纳法证明:当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24
(1)n=2时成立
1/n+1+1/n+2=7/12>13/24成立
(2)假设n=k时成立,即1/k+1+1/k+2+...+1/2k>13/24
n=k+1时,
1/k+2+1/k+3+...+1/2k+1/2k+1+1/2k+2
=1/k+1+1/k+2+...+1/2k+(1/2k+1+1/2k+2-1/k+1)
=1/k+1+1/k+2+...+1/2k+(1/2k+1-1/2k+2)>1/k+1+1/k+2+...+1/2k>13/24成立
根据(1),(2)当n>=2时,1/n+1+1/n+2+1/n+3+...+1/2n>13/24

n=2时成立。好证。假设n=k时成立,即1/k+1+1/k+2+...+1/2k>13/24
n=k+1时,1/k+2+1/k+3+...+1/2k+1/2k+1+1/2k+2>1/k+1+1/k+2+...+1/2k>13/24
得证。