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

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camperbot
2022-03-31 22:31:59 +05:30
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parent 01f5769190
commit a3a8b8cb5e
137 changed files with 557 additions and 310 deletions
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3
curriculum/challenges/chinese-traditional/10-coding-interview-prep/project-euler/problem-137-fibonacci-golden-nuggets.md
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@ -14,7 +14,8 @@ dashedName: problem-137-fibonacci-golden-nuggets
令人驚訝的是：
$$\begin{align} A_F(\frac{1}{2}) & = (\frac{1}{2}) × 1 + {(\frac{1}{2})}^2 × 1 + {(\frac{1}{2})}^3 × 2 + {(\frac{1}{2})}^4 × 3 + {(\frac{1}{2})}^5 × 5 + \cdots \\\\ & = \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \cdots \\\\ & = 2 \end{align}$$
$$\begin{align} A_F(\frac{1}{2}) & = (\frac{1}{2}) × 1 + {(\frac{1}{2})}^2 × 1 + {(\frac{1}{2})}^3 × 2 + {(\frac{1}{2})}^4 × 3 + {(\frac{1}{2})}^5 × 5 + \cdots \\\\
& = \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \cdots \\\\ & = 2 \end{align}$$
前五個對應的自然數 $x$ 如下。

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curriculum/challenges/chinese-traditional/10-coding-interview-prep/project-euler/problem-330-eulers-number.md
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@ -10,11 +10,13 @@ dashedName: problem-330-eulers-number
對於所有的整數 $n$，一個無限實數序列 $a(n)$ 定義如下：
$$ a(n) = \begin{cases} 1 & n < 0 \\\\ \displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases} $$
$$ a(n) = \begin{cases} 1 & n < 0 \\\\
\displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases} $$
例如，
$$\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e − 1 \\\\ & a(1) = \frac{e − 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e − 3 \\\\ & a(2) = \frac{2e − 3}{1!} + \frac{e − 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e − 6 \end{align}$$
$$\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e − 1 \\\\
& a(1) = \frac{e − 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e − 3 \\\\ & a(2) = \frac{2e − 3}{1!} + \frac{e − 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e − 6 \end{align}$$
其中，$e = 2.7182818\ldots$ 是歐拉常數。

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curriculum/challenges/chinese-traditional/10-coding-interview-prep/project-euler/problem-92-square-digit-chains.md
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@ -12,7 +12,8 @@ dashedName: problem-92-square-digit-chains
舉個例子：
$$\begin{align} & 44 → 32 → 13 → 10 → \boldsymbol{1} → \boldsymbol{1}\\\\ & 85 → \boldsymbol{89} → 145 → 42 → 20 → 4 → 16 → 37 → 58 → \boldsymbol{89}\\\\ \end{align}$$
$$\begin{align} & 44 → 32 → 13 → 10 → \boldsymbol{1} → \boldsymbol{1}\\\\
& 85 → \boldsymbol{89} → 145 → 42 → 20 → 4 → 16 → 37 → 58 → \boldsymbol{89}\\\\ \end{align}$$
可以發現，每條到達 1 或 89 的數鏈都會陷入循環。 最令人驚訝的是，從任意數字開始，數鏈最終都會到達 1 或 89。