A classic:
Show that
$$H_n = \sum_{k=1}^{n} \frac{1}{k}$$
is never an integer, for $n \gt 1$.
i.e.
$$ 1 + \frac{1}{2} + \dots + \frac{1}{n}$$
is never an integer for $n \gt 1$.
Show that
$$H_n = \sum_{k=1}^{n} \frac{1}{k}$$
is never an integer, for $n \gt 1$.
i.e.
$$ 1 + \frac{1}{2} + \dots + \frac{1}{n}$$
is never an integer for $n \gt 1$.
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