Find the radius of convergence, r, of the series. [infinity] n2xn 8 · 16 · 24 · ⋯ · (8n) n = 1

My best guess for what the series should be:

The denominator is the product of consecutive multiples of 8, and actually contains a factorial:

So the series is

From here, you can apply any of the applicable convergence tests. My personal go-to is the ratio test:

0 < 1, so the series converges for all .