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The limit comparison test states: an bn Suppose [an, [bn are series of positive terms and that L = lim % € (0, ∞). Then the series have the same convergence status (both converge or both diverge to ∞). 1 n² n (a) Use the limit comparison test with b₁ = to show that the series Σ In (1+1) converges. (Hint: Recall that e = lim (1 + ½)”) (b) Prove the limit comparison test. L (Hint: first show that ½ < a <31 for large n) an 2 bn 2 (c) What can you say about the series Σan and Σ bn if L = 0 or L = ∞? Explain.

The limit comparison test states: an bn Suppose [an, [bn are series of positive terms and that L = lim % € (0, ∞). Then the series have the same convergence status (both converge or both diverge to ∞). 1 n² n (a) Use the limit comparison test with b₁ = to show that the series Σ In (1+1) converges. (Hint: Recall that e = lim (1 + ½)”) (b) Prove the limit comparison test. L (Hint: first show that ½ < a <31 for large n) an 2 bn 2 (c) What can you say about the series Σan and Σ bn if L = 0 or L = ∞? Explain.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.4: Improper Integrals
Problem 37E
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The limit comparison test states: an bn Suppose [an, [bn are series of positive terms and that L = lim % € (0, ∞). Then the series have the same convergence status (both converge or both diverge to ∞). 1 n² n (a) Use the limit comparison test with b₁ = to show that the series Σ In (1+1) converges. (Hint: Recall that e = lim (1 + ½)”) (b) Prove the limit comparison test. L (Hint: first show that ½ < a <31 for large n) an 2 bn 2 (c) What can you say about the series Σan and Σ bn if L = 0 or L = ∞? Explain.
Transcribed Image Text:The limit comparison test states: an bn Suppose [an, [bn are series of positive terms and that L = lim % € (0, ∞). Then the series have the same convergence status (both converge or both diverge to ∞). 1 n² n (a) Use the limit comparison test with b₁ = to show that the series Σ In (1+1) converges. (Hint: Recall that e = lim (1 + ½)”) (b) Prove the limit comparison test. L (Hint: first show that ½ < a <31 for large n) an 2 bn 2 (c) What can you say about the series Σan and Σ bn if L = 0 or L = ∞? Explain.
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