证明:1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)

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证明:1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)
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证明:1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)
证明:1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)

证明:1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)
1/(3k+2)+1/(3k+3)+1/(3k+4)-1/(k+1) =[(3k+3)(3k+4)+(3k+2)(3k+4)+(3k+2)(3k+3) -3(3k+2)(3k+4)]/[(3k+2)(3k+3)(3k+4)] =2/[(3k+2)(3k+3)(3k+4)] 当k>0时 原式>0 即 1/(3k+2)+1/(3k+3)+1/(3k+4)>1/(k+1)