Of course Thanks!
I don't think induction is necessary. To show that this is always positive, show that the numerator and denominator are always the same sign (I can't see any reason why either of them would ever be negative...)
________________________
ipad ebooks
ipad comics
??The denominator is just $\displaystyle 2a_n$. Saying that "I can't see any reason why either of them would ever be negative" is exactly the same as saying "I can't see any reason why $\displaystyle a_n$ wouldn't be positive"- and that does NOT constitute a proof that it is!
Indeed, since the numerator, $\displaystyle a_n^2+ 2$ is obviously always positive, saying "show that the numerator and denominator are always the same sign" is exactly the same as saying "show that $\displaystyle a_n$ is always positive" which is exactly what the original problem says!