Question

What is the radius of convergence of `sum_1^oo (x-3)/n^(11/10)`?

Answer 1

Infinite

Explanation:

`int_1^oo 1/t^(11/10) dt=int_1^oo t^(-11/10) dt=[-10t^(-1/10)]_1^oo=10`

So `sum_1^oo 1/n^(11/10)` converges by the integral test.

So `sum_1^oo (x-3)/n^(11/10) = (x-3) sum_1^oo 1/n^(11/10)` also converges for any `x`