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gmn
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Homework Statement
show the sequence sn= (n+1)1/2 - n1/2 converges to zero
Homework Equations
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 - n1/2 = 1/((n+1)1/2 + n1/2). My question is that I show this goes to zero because sn<1/n(1/2) which goes to zero, but my professor provides a solution where he writes sn<1/2(n1/2). I don't understand why the 2 is there. Is saying that sn<1/(n1/2) insufficient or not true?
Thanks