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Provide short proofs for those that are true and counterexamples for any that are not. 1)...

Provide short proofs for those that are true and counterexamples for any that are not.

1) If  ∑∞n=0 an(2k-3)^n converges at k=4 , then it converges at k=(-1)

2) If   ∑∞n=0 an(2k-3)^n converges at k=4, then it diverges at k=(-1)

3) If ∑∞n=0 an(2k-3)^n converges at k=4, then its radius of convergence is R = 5/2

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