>>132854199>>132854984Infinity doesn't work that way. You can't talk about anything being out at infinity because you never reach infinity, just as you can't talk about the last digit of pi or the last 9 of 0.9999....
it doesn't work that way
The reason the pic fails is because during the change from the 2nd line to the 4th line you have redefined the series. It's always easy to do this when you use that kind of notation. But if you write it out correctly you can see the change. Originally the series was
sum_n (1-1)
By line 4 it has changed to
1 + sum_n (-1+1)
If you want to claim they are the same you'd have to formally prove it, which you can't because they aren't.
The sequence of sums for the first one is 0, 0, 0, .... while the sequence of sums for the second one is 1, 1, 1, ....
