Consider the recursive series
$ \; \ \quad \qquad a_1=0, \ a_i=a_{i-1}+b_{i-1}$
$ \; \ \quad \qquad b_1=1, \ b_i=b_{i-1}+2$
$ \ c_0 =0, \ c_1=4, \ c_i=a_ic_{i-2}+b_i c_{i-1}$
$d_0 =1, \ d_1=1, \ d_i=a_i d_{i-2}+b_i d_{i-1}$
What does the ratio $c_i/d_i$ converge to as $i \to \infty? $