That is equivalent to\pi=\sqrt{12}\sum_{n\geq0}\frac{(-1)^n}{3^n(2n+1)}

Olivia Vasquez

Olivia Vasquez

Answered question

2022-02-25

That is equivalent to
π=12n0(1)n3n(2n+1)

Answer & Explanation

mtakadamu9i5

mtakadamu9i5

Beginner2022-02-26Added 8 answers

Another answer:
π12=3arctan(13)
=301311+t2dt
=3013n=0(t2)ndt
=3n=0(1)n013t2ndt
=3n=0(1)n[t2n+12n+1]013
=3n=0(1)n2n+1((13)2n+10)
=33n=0(1)n(3)2n(2n+1)
=n=0(1)n3n(2n+1)
So
π=12n=0(1)n3n(2n+1)

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