show that $\displaystyle
\sum\limits_{k = 1}^n {\frac{1}
{{k^s }}} = \frac{1}
{{n^{s - 1} }} + s\int\limits_1^n {\frac{{\left[ x \right]}}
{{x^{s + 1} }}dx}
$
with s not equal to 1
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