Implications of zero row when row reducing matrix November 30    1

Often when I am performing elementary row operations to row reduce an arbitrary $A_{m \times n}$ matrix, a row of 0's appears, $[0 \, \, 0 \, ... \, 0\, \, 0]$.I am uncertain, does this imply either or both of the following:a row in $A$ is a linear c

Generalized Harmonic numbers November 30

I'd like to be able to prove the following inequality: $\frac{{{H_{n, - r}}}}{{{n^r}\left( {n + 1} \right)}} \le \frac{{{H_{n - 1, - r}}}}{{n{{\left( {n - 1} \right)}^r}}}$.It's clear that as $n \to \infty$ we get equality, the limit on each side is

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