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\item[(1)]$x$を正数とするとき，
$\displaystyle\log\left( 1+\frac{1}{x} \right)$と
$\displaystyle\frac{1}{x+1}$の大小を比較せよ．
\item[(2)]$\displaystyle{\left( 1+\frac{2001}{2002} \right)}^{\displaystyle\frac{2002}{2001}}$，
$\displaystyle{\left( 1+\frac{2002}{2001} \right)}^{\displaystyle\frac{2001}{2002}}$の大小を比較せよ．
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