How do you find the radius of convergence of the power series #Sigma (n!)/(n^n)x^(2n)# from #n=[1,oo)#?
The radius of convergence is
We can apply the ratio test, stating that a series:
is absolutely convergent if:
Calculate the expression of the ratio for this series:
Now we have:
The series is then absolutely convergent if:
which means the radius of convergence is