Gottfried Wrote:Refering to the header of this thread and your obvious love to iteration and trajectories, I challenge you to compute the alternating sum of all the intermediate steps of the trajectory

I, 2^I, 2^(2^I), 2^(2^(2^I)...

AS(2,I) = I - 2^I + 2^2^I - 2^2^2^I + ... -... = ??

My proposal is

AS(2,I) = -0.440033096027+0.928380628227*I

What do you think?

Gottfried

I can only say it diverges, and I understand You want me to find a method to sum it and a result. Unfortunately, I can not do it yet, but I am interested in 2^I in general and divergent series as well as they might be doing the same as tetration-somehow sending real numbers to complex domain , though the example I made with infinite logarithms ended in a kind of disaster as every base b ( except h(0) and h(1)) atracted to single value -W(-1). So let us keep Your result in mind while learn the basics in my strange ways-backwards

Ivars