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.

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