### A Pluto.jl notebook ### # v0.14.0 using Markdown using InteractiveUtils # ╔═╡ b2d786ec-7f73-11ea-1a0c-f38d7b6bbc1e md""" # The Basel problem _Leonard Euler_ proved in 1741 that the series ```math \frac{1}{1} + \frac{1}{4} + \frac{1}{9} + \cdots ``` converges to ```math \frac{\pi^2}{6}. ``` """ # ╔═╡ b2d79330-7f73-11ea-0d1c-a9aad1efaae1 n = 1:100000 # ╔═╡ b2d79376-7f73-11ea-2dce-cb9c449eece6 seq = n .^ -2 # ╔═╡ b2d792c2-7f73-11ea-0c65-a5042701e9f3 sqrt(sum(seq) * 6.0) # ╔═╡ Cell order: # ╟─b2d786ec-7f73-11ea-1a0c-f38d7b6bbc1e # ╠═b2d792c2-7f73-11ea-0c65-a5042701e9f3 # ╠═b2d79330-7f73-11ea-0d1c-a9aad1efaae1 # ╠═b2d79376-7f73-11ea-2dce-cb9c449eece6