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Does there exist a closed form expression for this sum?

$$ \sum\limits_{i=1}^n \frac {1}{i} $$

HF_
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  • Welcome to StackExchange! Please show what working you have done towards this and your motivation for wanting to know the answer, so people can tailor their answers to your level of knowledge – lioness99a May 10 '17 at 14:21

1 Answers1

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You would have to define what "closed" means. As far as I can tell, $\displaystyle \sum_{i=1}^n\frac1i$ is a closed as it can get.

Martin Argerami
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  • I think the OP mean the "primitive" of $a_n = \frac{1}{n}$. – user8469759 May 10 '17 at 14:23
  • Yes, I understand that. I usually try to fight the "closed form" attempts, because people are often misled by them. Many people will feel that $e^x$ is a "closed form" of $\sum_{k=0}^\infty \frac{x^k}{k!}$, when in reality you need the series to obtain values from the "closed form". Or you will find people looking for a "closed form" of $\int_0^xe^{-t^2},dt$, when this expression is very clear, and efficient for calculations. The point is that many "closed forms" are just names. – Martin Argerami May 10 '17 at 14:29