kill(all)$

top(n):=3*n^4+11*n^3 +12 *n^2 + 13*n-27;

bot(n):=n^6 +6*n^5 +22*n^4+48*n^3+85*n^2+90*n+84;

sum(top(n)/bot(n),n,1,inf);

factor(bot(n));

sum(1/n^2,n,1,inf),simpsum;

%pi/2;

top(x)/bot(x);

sum(top(n)/bot(n),n,1,inf),simpsum=true;