Answered

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Suppose [infinity] ∑ = 0 z has radius of convergence ∑[infinity]ₙ = 0 ₙzⁿ ∑[infinity]ₙ = 0 z 12 ∑[infinity]ₙ = 0 ( / )zⁿ ( ≠ 0) 1 2 2, 0 .
Show that () ∑[infinity]ₙ = 0 ⁿz has radius o convergence least 12 .

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