Find the radius of convergence if |3x+2| lim n-inf a_n

Question

Find the radius of convergence if |3x+2| lim n->inf  a_n <1, and the limit equals 1. The answer is {2/6}, but i dont understand why.  See complete problem below.

anonymous · Answer

$$|3x+2| \lim_{n \rightarrow \infty}  an <1$$
$$|3x+2| <1$$  = $$-1<3x+2< -1$$  = $$-1< x < -1/3$$  and some how, radius of convergence= {2/6}

amistre64 · Answer

radius of convergence is the distance from the midpoint to an and point

amistre64 · Answer

end point that is

amistre64 · Answer

as such, radius is going to be postive in value

amistre64 · Answer

now you sure its 2/6?  which equals 1/3

anonymous · Answer

Thats what he said and wrote on the board. Which is also y i was a bit confused. Its as if he multiplied spomething to get that number, even though I could just simply to get 1/3

anonymous · Answer

thats what i would have done. Teachers do unnecessary things sometimes

amistre64 · Answer

also, notice that the midpoint of -1 to -1/3

add and divide in half

1+1/3 = 4/3

4/3
---- = 4/6 = 2/3
  2

so the 2/6 might be a typo

anonymous · Answer

Ah, okay. Thanks!