^
2
^
k*a(2^
k*m)=1/(2^
k*m^
2)
^
2*sum(1/2^
k,k,0,+infinity)=2/m^
2
^
s, 2^
k*a(2^
k*m)=1/(2^
(k*(s-1))*m^
s)
^
s*sum((1/2^
(s-1))^
k,k,0,+infinity)
^
(s-1)/((2^
(s-1)-1)*m^
s)
^
2)
^
4)
^
(m-1)*b(m),1,+infinity)=
^
(m)*b(m+1),0,+infinity)
On choisit encore Digits:=20
pour s=2,
1/n2 =
/6
On tape :
t2(m):=2/(m+1)^
2
seriealt1(20,t2),evalf(pi^
2/6)
On obtient :
1.64493406684822645248, 1.64493406684822643645
On tape :
seriealt2(20,t2);seriealt3(20,t2);
On obtient :
1.64493374613777534516, 1.64493406688805599300
pour s=4,
1/n4 =
/90
On tape :
t4(m):=8/(7*(m+1)^
4)
seriealt1(20,t4);evalf(pi^
4/90)
On obtient :
1.08232323371113822384, 1.08232323371113819149
On tape :
seriealt2(20,t4);seriealt3(20,t4);
On obtient :
1.08232265198912440013, 1.08232323371697925335