Power series: Find the radius of convergence R of the series

Question

n=1 8^n(x+6)^n / sq root (n)

R=

find their interval of convergence I of the series. (Use interval notation)

I=

Answer 1

The interval of convergence is [ - 49/8 , -47/8)

The radius of convergence" R = 1/8

The alternating sign rule comes into play on the left end of the interval.

R = 1/8 (not R = 1) because of the factor of 8^n