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The Ratio Test (Calculus II)

Free printable university Calculus II worksheet on the ratio test: computing L = lim |a(n+1)/a(n)| for series with factorials, exponentials and powers, and concluding absolute convergence or divergence.

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Calculus II Β· Math worksheet
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Math

Calculus II: The Ratio Test

Compute L = lim |a(n+1)/a(n)| for each series. If L < 1 the series converges absolutely; if L > 1 (or L = ∞) it diverges; the test is inconclusive only when L = 1.

  1. 1.
    Use the ratio test to determine whether Σ[n=1 to ∞] 8n8^{n}/n! converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  2. 2.
    Use the ratio test to determine whether Σ[n=1 to ∞] 9n9^{n}/n! converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  3. 3.
    Use the ratio test to determine whether Σ[n=1 to ∞] n!/4n4^{n} converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  4. 4.
    Use the ratio test to determine whether Σ[n=1 to ∞] n!/6n6^{n} converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  5. 5.
    Use the ratio test to determine whether Σ[n=1 to ∞] n2n^{2}/2n2^{n} converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  6. 6.
    Use the ratio test to determine whether Σ[n=1 to ∞] n/3n3^{n} converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  7. 7.
    Use the ratio test to determine whether Σ[n=1 to ∞] 3n3^{n}/n2n^{2} converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
  8. 8.
    Use the ratio test to determine whether Σ[n=1 to ∞] 3n3^{n}/n converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
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