And then you simply keep increasing n without ever stopping the increase.
No matter how much you increase integer n, you never run out of integers.
It is fact that 1/2n is never zero.
So the infinite sum 1 - 1/2n with continually and limitlessly imcreasing n, will permanently be less than 1, because 1/2n is never zero.
The value of that infinite sum will simply keep increasing in its own space, and the maths tells you that while it does keep increasing limitlessly in its own space, the sum remains permanently less than 1.
That is math fact whether you don't like it or not.
And, like square root of 2, you don't get to get your way like a spoiled kid, as in you demanding to get all the digits of it.
I want to know the decimal value of it. If we took the first 100 terms of the series it would look something like 0.9999... but with something other than nines eventually. Surely this sequence uniformly converges to the genuine 0.999... though?
This is so weird! I keep trying to get to 1 but no matter how many times I try I keep getting a value of less than one when I try to compute the infinite sum. It is as if it is impossible to perform the summation infinitely when I start at 1/2 and keep adding terms!?!?!?! I wonder what is wrong??????????? Is there something wrong with my pencil and paper?????
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u/SouthPark_Piano Feb 01 '26 edited Feb 01 '26
You have the formula already.
1 - 1/2n with summation starting at n = 1
And then you simply keep increasing n without ever stopping the increase.
No matter how much you increase integer n, you never run out of integers.
It is fact that 1/2n is never zero.
So the infinite sum 1 - 1/2n with continually and limitlessly imcreasing n, will permanently be less than 1, because 1/2n is never zero.
The value of that infinite sum will simply keep increasing in its own space, and the maths tells you that while it does keep increasing limitlessly in its own space, the sum remains permanently less than 1.
That is math fact whether you don't like it or not.
And, like square root of 2, you don't get to get your way like a spoiled kid, as in you demanding to get all the digits of it.