Dangerous limits ... Tommy's limit paradox

[tommy1729]

Not so much related to tetration but I just wanted to warn about limits.

Limits , induction and infinity are imho poorly used and understood.

For a simple example

1/1 + 1/4 +1/9 + 1/16 + ...

The truncated sum after n additions is
Always rational. No matter how Large n is.

However the (complete) Sum = zeta(2) = irrational.

But that is Well known.

Tommy's limit paradox

Quiz

F(1) = 1/3
F(2) = 1/3 + 1/9 + 1/27
...

Is

(-2) ^( F(oo) ) =

A) sqrt(-2) = sqrt(2) i

Most students say " Yes ofcourse ! "

B) the solution set {sqrt(2) i , - sqrt (2) i )
C) (-2)^0,499999...
D) - 2^(1/4 + 1/8 + ...)
E) - sqrt(2)
F) cant say
G) other.

Regards

Tommy1729