chore: manual translations (#42811)

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Nicholas Carrigan (he/him)
2021-07-09 21:23:54 -07:00
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806 changed files with 8935 additions and 4378 deletions

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@ -8,7 +8,7 @@ dashedName: sum-of-a-series
# --description--
Compute the **n**<sup>th</sup> term of a [series](https://en.wikipedia.org/wiki/Series (mathematics)), i.e. the sum of the **n** first terms of the corresponding [sequence](https://en.wikipedia.org/wiki/sequence). Informally this value, or its limit when **n** tends to infinity, is also called the *sum of the series*, thus the title of this task. For this task, use: $S*n = \\sum*{k=1}^n \\frac{1}{k^2}$ and compute $S\_{1000}$ This approximates the [zeta function](https://en.wikipedia.org/wiki/Riemann zeta function) for S=2, whose exact value $\\zeta(2) = {\\pi^2\\over 6}$ is the solution of the [Basel problem](https://en.wikipedia.org/wiki/Basel problem).
Compute the **n**<sup>th</sup> term of a [series](https://en.wikipedia.org/wiki/Series (mathematics)), i.e. the sum of the **n** first terms of the corresponding [sequence](https://en.wikipedia.org/wiki/sequence). Informally this value, or its limit when **n** tends to infinity, is also called the *sum of the series*, thus the title of this task. For this task, use: $S_n = \displaystyle\sum_{k=1}^n \frac{1}{k^2}$.
# --instructions--