Chudnovsky algorithm

[compsystems]

PI_ (n):=((2.0*sqrt(2)/9801)*Σ((4*k)!*
(1103+26390*k)/((k!)^4*396^(4*k)),k,0,n))^(-1);

Why the evaluation at different values of n doesn't change the decimal values?

PI_ (1) [enter] 3.14159265359
PI_ (10) [enter] 3.14159265359
PI_ (34) [enter] 3.14159265359

[Valentin Albillo]

(08-17-2021 02:50 AM)compsystems Wrote:  PI_ (n):=((2.0*sqrt(2)/9801)*Σ((4*k)!*
(1103+26390*k)/((k!)^4*396^(4*k)),k,0,n))^(-1);

Why the evaluation at different values of n doesn't change the decimal values?

PI_ (1) [enter] 3.14159265359
PI_ (10) [enter] 3.14159265359
PI_ (34) [enter] 3.14159265359

First of all, this is one of Ramanujan formulae for computing Pi.

Secondly, you're not getting changes because just 1 term of the series already gives the accuracy your system allows. Use some multiprecision system and you'll see them change. Estas matando moscas a cañonazos.

V.