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Q: Find the radius of convergence of Σxⁿ/n! and Σn!xⁿ. Σxⁿ/n!: ratio: |aₙ/aₙ₊₁| = (n+1)!/n! = n+1 → ∞: R = ∞ (converges everywhere - eˣ!). Σn!xⁿ: ratio: n!/(n+1)! = 1/(n+1) → 0: R = 0 (converges only at x = 0!). Geometric Σxⁿ: R = 1 (|x|<1!).