find the range of values for x which the geometric series has a sum to infinity.

sorry i didnt know how to type the problem in here so i screen grab it from word

but incase you cant see the pic ill type the best i can

1- [(x-1)/3] + [(x-1)/3]^2 - [(x-1)/3]^3 + ..... if that makes sense

sorry my typing skills are not so great only just getting used to using word.

I some how calculated from many hrs that the range of x was between -1.7 to 0.7 but the lecturer told me that the numbers should be whole numbers and maybe with expressions he is quite vague on what im to do sorry if all this babble is of no help.