Tetration series for integer exponent. Can you find the pattern?
#8
I'm not that good on math, but....
I can help as a programmer.
Maybe precision problems are due to usage of "fixed" floating points (I mean fixed bit numbers).
There are libraries that can work with "big number" or "arbitrary precision".
For example GMP (this is a C/C++ library) gives non limited (limited by memory) number representation, so there is no problem with numbers like 10^(10^10) etc.

And MPFR library does similar thing for floating point numbers .....
I've written some tetration programs using those two, and they're much more precise, but at the horrible cost of memory and time.
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