kill(all)$

van=facebook.com/LearningCalculus$

a(i):=1/(2*i-1)^4$
b(i):=1/(2*i)^4$
create_list(a(i),i,1,4);
create_list(b(i),i,1,4);

sum(a(i),i,1,inf)/sum(b(i),i,1,inf);

       lookup sum in Wolfram et. al.

A:%pi^4/96; B: %pi^4/1440;

A/B;

AA:integrate(a(x),x,1,inf);
BB:integrate(b(x),x,1,inf);

AA/BB;