TITLE: Is "converges at" idiomatic English in some regions?
QUESTION [6 upvotes]: Some students write, e.g., "$\sum(1/n^2)$ converges at $\pi^2/6$", where I would write "converges to".
Are there regions of the English-speaking world where it is standard to say "converges at"? Or should this be considered a mistake made by non-native speakers of English?

REPLY [17 votes]: This is an error. Worse, there is a correct use for "converges at" which is not this. The following sentence shows a correct use of "converges at".

The sum $\sum_{n>0} \frac{x^n}{n^2}$ converges at $x=1$.

In other words, "converges at" refers to which value of some other parameter makes the sum converge, not to the value of the sum.