(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that [tex] 2( \sqrt{n+1} - \sqrt{n} ) < \frac{1}{ \sqrt{n}} < 2( \sqrt{n} - \sqrt{n-1}), n \in N [/tex]

2. The attempt at a solution

this works for n=1, but i'm entirely at a loss when trying to figure out which equations i can assume to be 'obviously' true (for the sake of the induction step), and what cannot be assumed..

All sides of the inequality eventually become 0, and while it seems fairly obvious to me that they all do it at an incrementally slower pace than the preceding one, i'm not sure what to make of this mathematically, or how to mold it into an equation expressing that.. can anyone lend a hand?

@radou: sorry, took a few mins to figure out what i'd done wrong

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# Inequality induction proof

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