#1 #I used the formula given in the "Samples of my Work" Section JesusG:=proc(N) local T: T:=sum(((-1)^n)*binomial(2*n, n)^5*(820*n^2+180*n+13)/(2^(20*n)), n=0..N): evalf(T); end: #want roughly 12.969 #Even for N as small as 4, this works really well! I got 12.96911151, and the true value (truncated appropriately) is 12.96911150. #2: #used Chudnovsky algorithm wikipedia article inside:=proc(j) return(evalf((-(6*j-1)*(2*j-1)*(6*j-5))/(10939058860032000*j^3))): end: ChudnovskyBros:=proc(N) local T, j, Acoeff, Baddend, Cprod, D, k, prodfactor: Acoeff:=1/(426880*evalf(sqrt(10005))): Baddend:=13591409: prodfactor:=1: #splitting up as advised_______ for k from 1 to N do prodfactor:=prodfactor*evalf(inside(k)): od: Cprod:=545140134*N+13591409: D:=Acoeff*(Baddend+prodfactor*Cprod): T:=1/D: return(evalf(T)): end: