#Homework by Mike Murr
#OK to post
#hw15
#read(`C15.txt`);

ud(3);
ud(4);


#PiJG(N): Computes Pi using the (series) formula on the home page of Jesus Guillera, and 
#         using the number of terms N in the series.
#
#         For 10000 decimal places, need 3334 terms, since we obtain 3 decimal places per term.
#
#         Prints one term of the series, every 500 terms, to display the convergence.
#
#with(combinat);

Digits:=10000;

PiJG:=proc(N) local n, term, accum, smallTerm, result;

accum:=13;

for n from 1 to N do
  term := ((-1)^n) * ((binomial(2*n,n))^5) * (820*n^2 + 180*n + 13)/2^(20*n);
  accum:=accum + term;
  if n mod 500 = 0 then
    smallTerm:= evalf(term);
    print(smallTerm);
  fi;
od;

#print(accum);

result:=evalf(sqrt(128/accum));

print(result);

end proc;

#PiJG(10);
#PiJG(20);
#PiJG(200);
#PiJG(3500);