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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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How to see the divergence of a series is not faster than some order? [closed]

$$ \sum_{m=1}^{n} m^{-1+1/p} \leq Cn^{1/p} $$ For $1<p<2$, I know the LHS is divergent but I can't see its speed of divergence is not faster than $n^{1/p}$.
Tak wa Ng's user avatar