Re: hot to write out this summation:

Am 01.07.2024 um 19:54 schrieb Chris M. Thomasson:

On 7/1/2024 10:12 AM, Moebius wrote:

I was just thinking that each iterate of the .(0)(1) is a real number...

Ok, you really make me laugh, sorry.
The point is that you are using an _undefined_ expression here.
It's like claiming [in the context of the real numbers] that 1/x tends to 1/0 as x tends to 0, or something like that.
I other words, there IS NO "iterate of the .(0)(1)" as there is no (referent of) ".(0)(1)". At least not in my book. :-P
You already wrote down what you meant:
r[0] = .01
r[1] = .0011
r[2] = .000111
r[3] = .00001111
...
Why not use the expression ".0...01...1" as a general "term" für your r's? Ok, we do not see that the number of "0"s is always identical with the numbers of "1" here.
Maybe a little diagram might be helpful:
. 0 ... 0 1 ... 1
   ------- -------
   n-times n-times
Starting with the index 1 we might (alternatively) state:
s[1] = .01
s[2] = .0011
r[3] = .000111
s[4] = .00001111
...
Then we'd have:
s[n] = . 0 ... 0 1 ... 1
          ------- -------
          n-times n-times
(for n = 1, 2, 3, ...).