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

show the sequence s_{n}= (n+1)^{1/2}- n^{1/2}converges to zero

2. Relevant equations

3. The attempt at a solution

I don't have that much of a problem showing the limit goes to zero, rationalize the numerator (or whatever it's called) to get (n+1)^{1/2}- n^{1/2}= 1/((n+1)^{1/2}+ n^{1/2}). My question is that I show this goes to zero because s_{n}<1/n(^{1/2}) which goes to zero, but my professor provides a solution where he writes s_{n}<1/2(n^{1/2}). I don't understand why the 2 is there. Is saying that s_{n}<1/(n^{1/2}) insufficient or not true?

Thanks

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# Technical question regarding showing sqrt(n+1) - sqrt(n) converges to 0

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