Toronto Math Forum
MAT3342018F => MAT334Tests => Term Test 1 => Topic started by: Victor Ivrii on October 19, 2018, 04:13:20 AM

Determine the radius of convergence
(a) $\displaystyle{\sum_{n=1}^\infty \frac{z^n}{2^n n^2}}$
(b) $\displaystyle{\sum_{n=1}^\infty \frac{z^{3n} (3n)!}{20^n (2n)! }}$
If the radius of convergence is $R$, $0<R< \infty$, determine for each $z\colon z=R$ if this series converges.

See the attached scanned picture.

Just a concern, it says in the problem that R should be positive.

I think the question means that if the radius of convergence is positive,you have to figure out whether the series is convergent at the radius of convergence. It doesn't mean the radius is always positive.

I think the question means that if the radius of convergence is positive,you have to figure out whether the series is convergent at the radius of convergence. It doesn't mean the radius is always positive.
Indeed.