Comparison & Limit Comparison Tests (Calculus II)
Free printable university Calculus II worksheet on the comparison and limit comparison tests: matching rational and radical terms to a p-series and concluding convergence or divergence.
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Calculus II · Math worksheet
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Math
Calculus II: Comparison & Limit Comparison Tests
For each series, choose a p-series that matches the terms' large-n behaviour, compute the limit of the ratio, and conclude convergence or divergence from the comparison series.
- 1.Use the limit comparison test to determine whether Σ[n=1 to ∞] (3)/(4n + 2) converges or diverges. State the comparison series you use.
- 2.Use the limit comparison test to determine whether Σ[n=1 to ∞] (3n + 4)/(3n^2 + 5) converges or diverges. State the comparison series you use.
- 3.Use the limit comparison test to determine whether Σ[n=1 to ∞] (4)/( + 8) converges or diverges. State the comparison series you use.
- 4.Use the limit comparison test to determine whether Σ[n=1 to ∞] (3n + 8)/( + 3) converges or diverges. State the comparison series you use.
- 5.Use the limit comparison test to determine whether Σ[n=1 to ∞] (4)/(4n^3 + 3) converges or diverges. State the comparison series you use.
- 6.Use the limit comparison test to determine whether Σ[n=1 to ∞] (3n + 9)/(3n^4 + 3) converges or diverges. State the comparison series you use.
- 7.Use the limit comparison test to determine whether Σ[n=1 to ∞] 1/(√n·(n + 6)) converges or diverges. State the comparison series you use.
- 8.Use the limit comparison test to determine whether Σ[n=1 to ∞] 1/ converges or diverges. State the comparison series you use.
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