#Please do post homework
#Jeffrey Tang, 3/11/25, Assignment 14 Pi edition!

JesusG := proc(N) local S, n:
    S := evalf(sum((-1)^n * binomial(2*n, n)^5 * (820*n^2 + 180*n + 13) / 2^(20*n), n = 0 .. N),500):
end:

# JesusG(10) shares 34 digits in common with 128/pi^2
# JesusG(100) shares 305 digits in common with 128/pi^2

# I will be attempting the Hackathon with Chudnovsky's Algorithm
ChudnovskyPi := proc(n) local i, numerator, denominator, term, sum_value, pi_approx:
    sum_value := 0:
    
    for i from 0 to n do
        numerator := factorial(6 * i) * (545140134 * i + 13591409);
        denominator := factorial(3 * i) * (640320^(3 * i + 3/2));
        term := (-1)^i * numerator / denominator;
        
        sum_value := sum_value + term;
    od;
    
    pi_approx := 12 * evalf(sum_value);
    
    evalf(1 / pi_approx);
end: