14. Sequences & Series

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) 1 / (√k × e^(√k))

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) (10ᵏ + 1) / k¹⁰

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from j = 1 to ∞) 5 / (j² + 4)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) 2⁹k / kᵏ

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) 5ᵏ(k!)² / (2k)!

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) 2ᵏ / (3ᵏ − 2ᵏ)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) k⁴ / (eᵏ⁵)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞) (4k)! / (k!)⁴

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)(⁵√k) / ⁵√(k⁷ + 1)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)(7ᵏ + 11ᵏ) / 11ᵏ

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)sin(1 / k⁹)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)cos(1 / k⁹)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)5¹⁻²ᵏ

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)k! / (kᵏ + 3)

11–86. Applying convergence tests Determine whether the following series converge. Justify your answers.

∑ (from k = 1 to ∞)tan⁻¹(1 / √k)