#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: