40–62. Choose your test Use the test of your choice to determine whether the following series converge.

∑ (k = 2 to ∞) 1 / (klnk)

40–62. Choose your test Use the test of your choice to determine whether the following series converge.

∑ (k = 1 to ∞) tan(1 / k)

40–62. Choose your test Use the test of your choice to determine whether the following series converge.

∑ (k = 1 to ∞) k⁸ / (k¹¹ + 3)

17–22. Integral Test Use the Integral Test to determine whether the following series converge after showing that the conditions of the Integral Test are satisfied.

∑ (k = 1 to ∞) 1 / (∛(5k + 3))

23–38. Divergence, Integral, and p-series Tests Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following series converge.

∑ (k = 3 to ∞) 1 / (k − 2)⁴

23–38. Divergence, Integral, and p-series Tests Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following series converge.

∑ (k = 1 to ∞) k / eᵏ

23–38. Divergence, Integral, and p-series Tests Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following series converge.

∑ (k = 1 to ∞) k^(–1/5)

23–38. Divergence, Integral, and p-series Tests Use the Divergence Test, the Integral Test, or the p-series test to determine whether the following series converge.

∑ (k = 1 to ∞) (k / (k + 10))ᵏ