#C14pi
Help14pi:=proc(): print(`Leibnitz(D1), LeibnitzN(N) `):end:

#Leibnitz(D1): computing Pi to D1 digits,i.e. the first time in the series where
#tuncating it gives a rational number appx. of pi with error <=10^(-D1)
#Pi=4*(1-1/3+1/5-1/7+...)=add(4*(-1)^i/(2*i+1)
Leibnitz:=proc(D1) local su,i:
su:=0:
for i from 0 while 4/(2*i+1)>1/10^D1 do
 su:=su+(-1)^i*4/(2*i+1):
od:
su:
end:

#LeibnitzN(N): using N terms in the Lebnitz formula to appx. Pi
LeibnitzN:=proc(N) local i:
evalf(add((-1)^i*4/(2*i+1),i=0..N)):
end: