If Σ n=1 -> ∞ an(x-1)^n converges at x = 4 and diverges at x = -2, then it converges at x = -1. TRUE OR FALSE?

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If Σ n=1 -> ∞ an(x-1)^n converges at x = 4 and diverges at x = -2, then it converges at x = -1. TRUE OR FALSE?

[From: ] [author: ] [Date: 14-05-12] [Hit: ]

Hence, it is true that it converges at x = -1.For our purposes, its irrelevant to know it diverges at x = -2.is this a Quadratic equation? or a potion formula?......

Please explain as well. Thanks!

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This is a power series about 1. Since it converges at x = 4, its radius of convergence is at least 4 - 1 = 3. So, the series surely converges on (1 - 3, 4] = (-2, 4]. Hence, it is true that it converges at x = -1.

For our purposes, it's irrelevant to know it diverges at x = -2.

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is this a Quadratic equation? or a potion formula?

1

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