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fix(curriculum): clean-up Project Euler 321-340 (#42988)

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* fix: clean-up Project Euler 321-340

* fix: typo

* fix: corrections from review

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>

* fix: corrections from review

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>
Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
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2021-07-29 20:59:06 +02:00
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35
curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-330-eulers-number.md
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@ -8,30 +8,37 @@ dashedName: problem-330-eulers-number
# --description--
An infinite sequence of real numbers a(n) is defined for all integers n as follows:
An infinite sequence of real numbers $a(n)$ is defined for all integers $n$ as follows:
<!-- TODO Use MathJax and re-write from projecteuler.net -->
$$ a(n) =
\begin{cases}
1 & n < 0 \\\\
\displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0
\end{cases}
$$
For example,a(0) = 11! + 12! + 13! + ... = e − 1 a(1) = e − 11! + 12! + 13! + ... = 2e − 3 a(2) = 2e − 31! + e − 12! + 13! + ... = 72 e − 6
For example,
with e = 2.7182818... being Euler's constant.
$$\begin{align}
& a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e − 1 \\\\
& a(1) = \frac{e − 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e − 3 \\\\
& a(2) = \frac{2e − 3}{1!} + \frac{e − 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e − 6
\end{align}$$
It can be shown that a(n) is of the form
with $e = 2.7182818\ldots$ being Euler's constant.
A(n) e + B(n)n! for integers A(n) and B(n).
It can be shown that $a(n)$ is of the form $\displaystyle\frac{A(n)e + B(n)}{n!}$ for integers $A(n)$ and $B(n)$.
For example a(10) =
For example $\displaystyle a(10) = \frac{328161643e − 652694486}{10!}$.
328161643 e − 65269448610!.
Find A(109) + B(109) and give your answer mod 77 777 777.
Find $A({10}^9)$ + $B({10}^9)$ and give your answer $\bmod 77\\,777\\,777$.
# --hints--
`euler330()` should return 15955822.
`eulersNumber()` should return `15955822`.
```js
assert.strictEqual(euler330(), 15955822);
assert.strictEqual(eulersNumber(), 15955822);
```
# --seed--
@ -39,12 +46,12 @@ assert.strictEqual(euler330(), 15955822);
## --seed-contents--
```js
function euler330() {
function eulersNumber() {
return true;
}
euler330();
eulersNumber();
```
# --solutions--