Quod Erat Demonstrandum

2008/01/14

[AL][PM] Hyperpower function

Filed under: HKALE,Pure Mathematics,University Mathematics — johnmayhk @ 4:39 下午

Justin asked me again about the hyperpower function. Sorry, I just re-post my old message in my old forum, which was prohibited by the adminstrators in the hkedcity. It is known that the following

converges if and only if

To know more about the hyperpower function, please visit the following

http://www.faculty.fairfield.edu/jmac/ther/tower.htm
http://mathworld.wolfram.com/PowerTower.html

We may create an AL pure mathematics question concerning hyperpower function like

Let
(a) Prove that {x_n} is increasing.
(b) By M.I. or otherwise, show that {x_n} is bounded above by 2.
(c) Hence solve the outdated problem:

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