Suppose that a_k >= 0 and a_k^(1/k) → a as k → ∞. Prove that ∑ (k=1 to ∞) a_kx^k converges absolutely for all abs (x) < 1/a if a ≠ 0 and for all x in R if a=0.

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- November 26th 2007, 12:18 PMtaypezabsolute convergence
Suppose that a_k >= 0 and a_k^(1/k) → a as k → ∞. Prove that ∑ (k=1 to ∞) a_kx^k converges absolutely for all abs (x) < 1/a if a ≠ 0 and for all x in R if a=0.

Thanks. - November 26th 2007, 03:51 PMPlato
- November 26th 2007, 07:04 PMThePerfectHacker