Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

I'm guessing the series is supposed to be



By the ratio test, the series converges if the following limit is less than 1.



The first terms in the numerator's denominator cancel with the denominator's denominator:



also cancels out and the remaining factor of can be pulled out of the limit (as it doesn't depend on ).



which means the series converges everywhere (independently of ), and so the radius of convergence is infinite.