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In the cloud (experimental)

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On your computer

(Recommended if you want to store your changes.)

  1. Copy the notebook URL:
  2. Run Pluto

    (Also see: How to install Julia and Pluto)

  3. Paste URL in the Open box

Frontmatter

If you are publishing this notebook on the web, you can set the parameters below to provide HTML metadata. This is useful for search engines and social media.

Author 1

z

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md"$z$"
129 μs

a b

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md"a
$\require{physics}$
b"
182 μs

The Basel problem

Leonard Euler proved x in 1741 that the series

11+14+19+⋯

converges to

O⁡(R)xπ26

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md"# The Basel problem

_Leonard Euler_ proved $x$ in 1741 that the series

$$\frac{1}{1} + \frac{1}{4} + \frac{1}{9} + \cdots$$

converges to

$$\order{R}{x} \frac{\pi^2}{6}$$"
303 μs
3.1415831043264424
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sqrt(sum(seq) * 6.0)
71.3 μs
1:100000
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n = 1:100000
15.3 μs
seq = n .^ -2
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59.5 ms

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67.2 μs