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anemone
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Prove that for all integers $k>1$:
$\left(\dfrac{1+(k+1)^{k+1}}{k+2}\right)^{k-1}>\left(\dfrac{1+k^k}{k+1}\right)^{k}$
$\left(\dfrac{1+(k+1)^{k+1}}{k+2}\right)^{k-1}>\left(\dfrac{1+k^k}{k+1}\right)^{k}$