Question

Find the set of the convergence of the power series?

Answer 1

First of all you want to seperate the expression into the distinct parts of a power series \[1/(4^n+3^n)\] and \[(x-3)^{2n}\]

Answer 2

So \[\sum_{n=1}^{\infty} (1/(4^n+3^n))(x-3)^{2n}\]

Answer 3

Next we need to determine the radius of converge of this series R

Answer 4

Do you know how to find the radius of convergence?

Answer 5

Well the radius of convergence is x=a so in this case x=3

Answer 6

Usually with power series we can use the ratio or the root test

Answer 7

So using the ratio test... we consider the value of L which is