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

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Answer 1 · 2015-11-29T09:01:43

Infinite

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

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 $x$

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