#Please do not post homework
#Salman Manzoor 03-12-2025, Assignment 14pi

#Plouffe (2006) formula exactly equal to pi
estPi:=proc(n) local i:
evalf(add( (1/i)*(72/(foo(i))-96/(foo(2*i))+24/(foo(4*i))),i=1..n)):
end:

# Andrew Fraker (2014) estimates e^pi around (5^4/3^3)
# we approximate foo_true(i) = 1/(e^(Pi*x)-1)

foo:=proc(x)
evalf(1/((5^4/3^3)^x-1)):
end:

JesusG:=proc(N) local n,i:
if evalb(N=1) then RETURN(13): fi:
evalf(13 + add(    (-1)^n * (product(2*i-1,i=1..n)/product(2*i-1,i=1..n) )^5 *
( 20*n*(9+41*n) +13 ) / 2^(10*n)  , n=1..N-1  )) :
end: