chore(i18n,learn): processed translations (#45583)

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camperbot
2022-03-31 22:31:59 +05:30
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137 changed files with 557 additions and 310 deletions

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@ -10,11 +10,13 @@ dashedName: problem-330-eulers-number
Una sequenza infinita di numeri reali $a(n)$ è definita per tutti gli interi $n$ come segue:
$$ a(n) = \begin{cases} 1 & n < 0 \\\\ \displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases} $$
$$ a(n) = \begin{cases} 1 & n < 0 \\\\
\displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases} $$
Per esempio,
$$\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e 1 \\\\ & a(1) = \frac{e 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e 3 \\\\ & a(2) = \frac{2e 3}{1!} + \frac{e 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e 6 \end{align}$$
$$\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e 1 \\\\
& a(1) = \frac{e 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e 3 \\\\ & a(2) = \frac{2e 3}{1!} + \frac{e 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e 6 \end{align}$$
dove $e = 2.7182818\ldots$ è costante di Euler.