Question

What is the interval of convergence of #sum_1^oo ln(n)/e^n (x-e)^n #?

Answer 1

`abs((x-e)/e)<1`

Explanation:

`((x-e)/e)^n < log(n)((x-e)/e)^n <(n+1)((x-e)/e)^n=ed/(dx)((x-e)/e)^(n+1)`

so the series is convergent for

`abs((x-e)/e)<1`