Problems

Test the following series for convergence.

Use the Integral Test to determine whether the following improper integrals converge or diverge.

41            Prove that if each a_n is positive and Y^= i ^an converges, then £_n'_{= t} <*l converges.

42            Using Theorem 1 (page 539), prove that a negative term series either converges or diverges to -∞.