#not OK to post homework
#Nick Belov, March 12 2025, Assignment 14

JesusG:=proc(N)
sum((-1)^n*binomial(2*n,n)^5*(820*n^2+180*n+13)/(2^(20*n)), n=0..N):
end:
#eval(abs(JesusG(10) - 128/pi^2))=10^-8
#JesusG(eval(abs(JesusG(100) - 128/pi^2))) was also 10^8
#infact Jesus of everything after 5 was 10^-8 so i imagine thats the point
#where the accuracy exceeds the capability of floating point arithmatic 


#pi approximation:

evalf((🥧:=3+sin(3))+sin(🥧));

#I found the idea for this here https://codegolf.stackexchange.com/questions/22009/pi-calculation-code-golf
#I hard coded two iterations of newtons method in as few characters possible.