>>11412137 is indeterminate in many forms depending on . So the question really is "why can't I cancel out the n's"
For the same reason you cannot associate infinitely many terms.
According to the associative law of addition only states that .
It is a theorem that needs to be proved that more that is unique, and it can be proved (by induction, also a given) for any natural number of terms, but it cannot be proved and is in fact false for infinitely many terms.
The Distributive law is similar, in that it is also a given law of arithmetic, where whether it holds for finitely many more terms is a theorem that needs to be proved (and can be by induction) and is in fact false for infinitely many terms
(your picture is actually a counter example which was probably used historically as an argument for an axiomatic treatment of math)
