Sequence Limits & the Divergence Test (Calculus II)
Free printable university Calculus II worksheet on sequence convergence: finding the limit of a(n) as n approaches infinity, and applying the divergence (nth-term) test to infinite series.
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Calculus II Β· Math worksheet
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Calculus II: Sequence Limits & the Divergence Test
Find the limit of each sequence as n β β, or show it diverges. For the series questions, apply the divergence test: if the terms do not approach 0 the series diverges; if they do approach 0 the test is inconclusive.
- 1.Determine whether the sequence aβ = ( + 5)/(7n^2 + 5) converges or diverges as n β β. If it converges, state the limit.
- 2.Determine whether the sequence aβ = (8n^2 + 7n + 8)/(5n^2 + 9) converges or diverges as n β β. If it converges, state the limit.
- 3.Determine whether the sequence aβ = (2n + 9)/(5n^2 + 9) converges or diverges as n β β. If it converges, state the limit.
- 4.Determine whether the sequence aβ = (4n^2 + 3n + 1)/(2n + 6) converges or diverges as n β β. If it converges, state the limit.
- 5.Determine whether the sequence aβ = converges or diverges as n β β. If it converges, state the limit.
- 6.Determine whether the sequence aβ = converges or diverges as n β β. If it converges, state the limit.
- 7.Apply the divergence test to the series Ξ£[n=1 to β] (n + 5)/(2n + 6). What can you conclude?
- 8.Apply the divergence test to the series Ξ£[n=1 to β] (6n + 2)/(4n + 1). What can you conclude?
- 9.Apply the divergence test to the series Ξ£[n=1 to β] (3n + 8)/( + 6). What can you conclude?
- 10.Apply the divergence test to the series Ξ£[n=1 to β] (7n + 8)/(8n^2 + 9). What can you conclude?
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