Sequences of Series

Question

I was given this summation problem and we were asked to find the interval of convergence. I think that R= 8, but I do not know how to do the interval of convergence. I tried (0,4) and (-4, 4), but was still getting it wrong. Are you able to show how to solve this problem? Thanks!

Answer 1

for x=0, 1st term is 1/1 = 1

for x=1 2nd term = 5/8 = .625

for x=2 3rd term = 36/64 = 9/16 = .5625

for x =3 4th term = 7^3/8^3 = 343/512 = .67

x=4, 5th term = 8^4/8^4 = 1

x=5, 6th term = 9^5/8^5 = 59049/32768 = 1.802

x=6 7th term = 10^6/8^6 = 1,000,000/262,144= 3.815

radius of convergence = 8

interval of convergence (-12, 4)

the sum doesn't converge, it approaches infinity

the terms approach infinity