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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.2011-10-27

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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.

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    @idmercer: is it possible that one of the lecturers, TA's, tutors, etc who taught them used the phrase "converges at" in this way?2011-11-22