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Problem 10.8.7
1–10. Choosing convergence tests Identify a convergence test for each series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test.
∑ (from k = 1 to ∞) (k² / (k⁴ + k³ + 1))
Problem 10.8.61
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 1 to ∞) 1 / ln(eᵏ + 1)
Problem 10.8.65
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 1 to ∞) (cos(1 / k) – cos(1 / (k + 1)))
Problem 10.8.67
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from j = 1 to ∞) cot(–1 / j) / 2ʲ
Problem 10.8.69
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 1 to ∞) (1 + 1 / (2k))ᵏ
Problem 10.8.71
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 1 to ∞) (ln²k) / k³ᐟ²
Problem 10.8.73
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 0 to ∞) k² · 1.001⁻ᵏ
Problem 10.8.77
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 0 to ∞) 3k / ∜(k⁴ + 3)
Problem 10.8.81
11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.
∑ (from k = 1 to ∞) (1 / √(k + 2) – 1 / √k)