Question

test convergence for 1/n*tan(1/n)

Answer 1

Apply the root test. limn→∞ |an| 1/n = limn→∞ n 2 + 1 2n2 + 1n 1/n = limn→∞ n 2 + 1 2n2 + 1 = 1 2 < 1. It follows that the series must converge absolutely