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Card 7 / 7:
limit comparison test
suppose a n , b n ≥ 0 for all n ≥ 1 . If lim n → ∞ a n / b n → L ≠ 0 , then ∑ n = 1 ∞ a n and ∑ n = 1 ∞ b n both converge or both diverge; if lim n → ∞ a n / b n → 0 and ∑ n = 1 ∞ b n converges, then ∑ n = 1 ∞ a n converges. If lim n → ∞ a n / b n → ∞ , and ∑ n = 1 ∞ b n diverges, then ∑ n = 1 ∞ a n diverges
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