Consider a power series ${\displaystyle \underset{n=0}{\overset{}{}}}{c}_n(x+1{)}^n.$ Some partial information is known.

Each $c_n$ is a positive constant for all $n0.$

$\underset{n}{lim}{c}_n{4}^n=.$

The series is convergent if we substitute $x=-6$ into the series.

Determine the radius of convergence of the series. If the series is convergent for every real number $x,$ then

enter $-1$ due to eClass technical restrictions.

Use a calculator to find a numerical approximation of your final answer to $2$ decimal places. For example, if your

final answer is $,$ then you should enter $3\mathrm{.}14$ in the box below. In tests and the final exam, you will NOT need to

approximate your final answer numerically.

Answer: