Newton’s Formula for ∏
Newton invented the following formula in 1684, though he never published. Later, it was discovered independently by others, including Euler:
![\[\frac{\pi}{2}=\sum_{k=0}^{\infty}\frac{k!}{(2k+1)!!}\]](https://oopstart.com/wp-content/ql-cache/quicklatex.com-980277b870ce7ba16b0042c811830cce_l3.png "Rendered by QuickLaTeX.com")
where 
means “double factorial”:
![\[n!!=n(n-2)(n-4)(n-6)\,...\,2\,or\,1\]](https://oopstart.com/wp-content/ql-cache/quicklatex.com-f5ba93cae646e4e518f91720745c82fd_l3.png "Rendered by QuickLaTeX.com")
![\[0!!\equiv 1\]](https://oopstart.com/wp-content/ql-cache/quicklatex.com-98c10991d5528ae10c70ed9aeb66b24c_l3.png "Rendered by QuickLaTeX.com")
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