# Is “converges at” idiomatic English in some regions?

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?

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I would expect it to be used in contexts such as "$\sum_k \frac{x^k}{k!}$ converges at 2", meaning that if we set $x=2$ then the resulting series converges. –  Henning Makholm Oct 27 '11 at 17:22

The sum $\sum_{n>0} \frac{x^n}{n^2}$ converges at $x=1$.
@Asaf, better square that $n$ in the denominator. –  Gerry Myerson Oct 27 '11 at 23:40
Strictly speaking, $f(x)=\sum_{n=1}^\infty\dfrac{1}{n^2}$ converges at $x=\dfrac{\pi^2}{6}$, it also converges to $\dfrac{\pi^2}{6}$ at that point... :-) –  Asaf Karagila Oct 27 '11 at 23:44