series convergent or divergent?
i have the series sigma n=1 to infinity (x-4)^n
wasn't sure how to manipulate this to make it a geometric sequence so i used the divergence test saying lim n-->infinity (x-4)^n
i got that it was divergent but not sure if i approached it correctly. please help!
Comments
You and your reasoning are correct.
It is not clear whether you are referring to a sequence or a series, but either way convergence depends on the value of x.
On the interval (3, 5), the sequence and the series converge.
For x = 5, the sequence is a constant 1, and the series diverges.
On (-∞, 3] or (5, ∞), both the sequence and the series diverge.