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
Name
Date
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 = β) it diverges; the test is inconclusive only when L = 1.
- 1.Use the ratio test to determine whether Ξ£[n=1 to β] /n! converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 2.Use the ratio test to determine whether Ξ£[n=1 to β] /n! converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 3.Use the ratio test to determine whether Ξ£[n=1 to β] n!/ converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 4.Use the ratio test to determine whether Ξ£[n=1 to β] n!/ converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 5.Use the ratio test to determine whether Ξ£[n=1 to β] / converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 6.Use the ratio test to determine whether Ξ£[n=1 to β] n/ converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 7.Use the ratio test to determine whether Ξ£[n=1 to β] / converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
- 8.Use the ratio test to determine whether Ξ£[n=1 to β] /n converges or diverges. State the value of L = lim |a(n+1)/a(n)|.
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