Question

Need help with determining radius of convergence

Answer 1

ratio test should get it quickly , almost in your head

Answer 2

compute \[\lim_{n\to \infty}|\frac{a_{n+1}}{a_n}|\]

Answer 3

do some algebra first, but not much \[\frac{(x+2)^{n+1} \sqrt{n}}{\sqrt{n+1}(x+2)^n}\] is the first step

Answer 4

you are stuck with \[\frac{\sqrt{n}}{\sqrt{n+1}}\] but when you divide you have \(|x+2|\) by itself in the numerator
then take the limit as \(n\to \infty\)

Answer 5

what do you get for the limit?