Suppose that the power series infinity sigma n=0 cn(x-5)^n converges when x = 2

Question

Suppose that the power series infinity sigma n=0 cn(x-5)^n converges when x = 2 and diverges when x = 10. From the above information, which of the following statements can we conclude to be true ? The radius of convergence R satisfies 3 LE R LE 5. We can NOT determine the interval of convergence from the above information only. The derivative of the power series is infinity sigma n=1 ncn(x-5)^n-1 which converges when x = 3. I and II only. I and III only. II and III only. All of the above. None of the above.

Explanation / Answer

converges when x=2 is true.

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