试证:对任意正整数n>1,有1/(n+1)+1/n+2+.+1/2n>1/2

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试证:对任意正整数n>1,有1/(n+1)+1/n+2+.+1/2n>1/2
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试证:对任意正整数n>1,有1/(n+1)+1/n+2+.+1/2n>1/2
试证:对任意正整数n>1,有1/(n+1)+1/n+2+.+1/2n>1/2

试证:对任意正整数n>1,有1/(n+1)+1/n+2+.+1/2n>1/2
n=2 时
1/3+1/4=7/12>1/2
设n=k时成立
即 1/(k+1)+1/(k+2)+.1/(2k)>1/2
n=k+1时
1/(k+2)+1/(k+3)+.1/(2k)+1/(2k+1)+1/(2k+2)>1/(k+2)+1/(k+3)+.1/(2k)+1/(2k+2)+1/(2k+2)=1/(k+1)+1/(k+2)+.1/(2k)>1/2

归纳验证略
当n=k(k>1)时,1/(k+1)+1/(k+2)+...+1/2k>1/2,假设成立
当n=k+1时,左式=1/(k+2)+1/(k+3)+...+1/2k+1/(2k+1)+1/(2k+2)
>1/2-1/(k+1)+1/(2k+1)+1/(2k+2)
=1/2+1/2(k+1)(2k+1...

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归纳验证略
当n=k(k>1)时,1/(k+1)+1/(k+2)+...+1/2k>1/2,假设成立
当n=k+1时,左式=1/(k+2)+1/(k+3)+...+1/2k+1/(2k+1)+1/(2k+2)
>1/2-1/(k+1)+1/(2k+1)+1/(2k+2)
=1/2+1/2(k+1)(2k+1).....通分
>1/2
其他步骤按格式写写就行。

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