Boundedness of $a+\frac 1a$ when iterated Here's something I was wondering... 

Is $$a + \frac 1a$$ for any positive real number $a$ bounded when iterated? 

For example,, if we start at $a=1$, continuing gives us $a= 1+ \frac 11=2$, then $a=2+\frac 12=2.5$ and so on. A quick program shows that it seems to grow without bound, but how would one prove this mathematically? If it is possible that is... Any hints would be appreciated.

Hint: Assume it has a bound $A$, then show that it will eventually exceed that bound.
