Question

find the radius and interval of convergence for the following series:

summation(from one to infinite) of (9-1)^n))*((x-3)^n)/n

Answer 1

(9-1)^(n)*((x-3)^(n))/(n)

Subtract 1 from 9 to get 8.
(8)^(n)*((x-3)^(n))/(n)

Multiply the rational expressions to get ((8)^(n)(x-3)^(n))/(n).
((8)^(n)(x-3)^(n))/(n)

Answer 2

oops. That 9 wasnt supposed to be in there...(-1)^n))*((x-3)^n)/n. Thats what it should be. Haha, sorryyy.

Answer 3

(-1)^(n)*((x-3)^(n))/(n)

Multiply the rational expressions to get ((-1)^(n)(x-3)^(n))/(n).
((-1)^(n)(x-3)^(n))/(n)

Answer 4

Are you sure? I thought that you use the ratio test and plug in n+1 every time there's an n....