MHB Prove 1/√n Inequality by Induction

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Prove this inequality by induction for all nEN:

1/√1 + 1/√2 + 1/√3 + ... + 1/√n >= √n
 
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I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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