Question

if i use the ratio test and get for the limit of a power series |x/9| how do i get the radius of convergence?
series is centered at 0

Answer 1

you get
\[|\frac{x}{9}|\]?

Answer 2

then just make sure
\[|\frac{x}{9}|<1\] i.e
\[-9<x<9\]

Answer 3

radius of convergence is
\[(-9,9)\]

Answer 4

you have to check the endpoints separately though,

Answer 5

well the radius would be 9 then righ?

Answer 6

so my answer is not complete

Answer 7

"radius of convergence" i believe actually means the interval over which it converges, but i guess as a "radius" it would be 9 yes. usually when someone asks for "radius of convergence" in my experience the question is really "over what interval does it converge?"

Answer 8

i have qustions asking for interval of convergence and some asking for radius of convergence

Answer 9

i could easily be wrong so don't take my word for it. but yes, the "radius" is 9

Answer 10

ok then radius in 9. the word "radius" makes a lot more sense when you are working with complex numbers.

Answer 11

if it asks for "interval" don't forget to check the endpoints

Answer 12

i don't know what your original problem was, but it could either converge or diverge at x = -9 and at x =9. you have to check those individually