Recent content by mxwlljack
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Undergrad Proof of Asymptotic Equality: $\sum_{n=0}^\infty a_n\frac{x^n}{n!} \sim ae^x$
If (a_n\to a), write [ \sum_{n\ge0}a_n\frac{x^n}{n!} =ae^x+\sum_{n\ge0}(a_n-a)\frac{x^n}{n!}. ] Since (a_n-a\to0), the second sum is (o(e^x)). Hence [ \boxed{\sum_{n\ge0}a_n\frac{x^n}{n!}\sim ae^x\quad(x\to\infty).} ]- mxwlljack
- Post #3
- Forum: Math Problem of the Week
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Latest Notable AI accomplishments
It’s fascinating to look back at how quickly AI was already progressing in 2018. The SQuAD results were a good example of AI moving beyond games and into practical language understanding and information retrieval. What stands out to me is how improvements in computing power, data, and...- mxwlljack
- Post #104
- Forum: Programming and Computer Science