Need help proving series is unbounded: a_{n+1} = 1/(a_{n}) + a_{n}

[Fiestar]

We have been given a series (a_{n}), where a_{1} > 0 and according to ever every possible n

a_{n+1} = 1/(a_{n}) + a_{n}.

We have to prove that (a_{n}) is unbounded.

So usually I would use subseries to do it. However I am not quite sure where to begin and where I should end up with.

 

[tkhunny]

Please show your efforts. Is \(\displaystyle a_{n}\) a subseries or a single term? Be specific.

Have you considered \(\displaystyle \dfrac{1}{a_{n}}+a_{n} = \dfrac{1 + \left(a_{n}\right)^{2}}{a_{n}}\)