1+(31×21)+(31×34×221×2!1)+(31×34×37×231×3!1)+⋯n terms
For natural numbers n, let Sn be the value of the above expression
Suppose that for positive integers a,b,c,d with gcd(a,b)=gcd(c,d)=1, we have
n→∞limSn=(ba)dc
What is the value of a+b+c+d?