Descubridor: Arquímedes (287-212 BC) averiguó que 3 10/71 < PI < 3 1/7

PI = 3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...

La fórmula de Vieta

2/PI = 2/2 * ( 2 + 2 )/2 * (2 + ( ( 2 + 2) ) )/2 * ...c

La fómula de Leibnitz

PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ...

El producto de Wallis

PI/2 = 2/1 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * ...

2/PI = (1 - 1/2^2)(1 - 1/4^2)(1 - 1/6^2)...

La fórmula de Lord Brouncker

4/PI = 1 +        1

           ----------------

           2 +     3^2

               ------------

               2 +   5^2

                  ---------

                  2 + 7^2 ...

(PI^{^2})/8 = 1/1^{^2} + 1/3^{^2} + 1/5^{^2} + ...

(PI^{^2})/24 = 1/2^{^2} + 1/4^{^2} + 1/6^{^2} + ...

La fórmula de Euler

(PI^{^2})/6 = (n = 1..) 1/n^{^2} = 1/1^{^2} + 1/2^{^2} + 1/3^{^2} + ...

(o mas generalmente...)

(n = 1..) 1/n^{^(2k)} = (-1)^{^(k-1)} PI^^(2k) 2^{^(2k)} B_(2k) / ( 2(2k)!)

B_(k) = el k ^th Número Bernoulli. ej. B₀=1 B₁=-1/2 B₂=1/6 B₄=-1/30 B₆=1/42 B₈=-1/30 B₁₀=5/66. Números Bernoulli adicionales se definen como (n 0)B₀ + (n 1)B₁ + (n 2)B₂ + ... + (n (n-1))B_(N-1) = 0 presumiendo que todos los Números impares de Bernoulli >1 son = 0. (n k) = coeficiente de binómico = n!/(k!(n-k)!)

 
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