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A:

Here’s the workaround that I’ve used: I downloaded the tar.gz files directly and extracted them in my WSL environment. Then I symlinked the directory directly and everything started working.

Q:

How to learn the mathematical definition of Euler’s constant?

Euler’s constant $\gamma$ has a series representation:
$$
\gamma = \sum_{n=1}^\infty \frac{1}{n!}
$$
How can one prove that this series converges without using a calculator? (Suppose one is too lazy to even open a calculator.)
What is the most effective way of learning the definition?

A:

There are two approaches to this: either you can use mathematical induction, or you can use the Cauchy product. We’ll start with the Cauchy product:
We first note that since the sequence is constant, i.e. of the form $(a,a,a,a,\ldots)$, the only possible terms to add are of the form $1/\prod_{i=1}^n p_i^{s_i}$ where $p_1,\ldots,p_n,p$ are distinct primes. Thus, we get
$$
\sum_{n=1}^\infty \frac{1}{n!} = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots
$$
Now, we perform the Cauchy product of the sequence
$$
\left(\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots,\frac{1}{1!}, \frac{1}{1!},\frac{1}{1!},\ldots\right)

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