I shall be very grateful to anyone who can guide me regarding the solution of the following problems.

Show that if Xn converges to X in rth mean ( r>=1), then E ( |Xn^r| )converges to E ( | X ^r |)

Show that if Xn converges to X in rth mean with r=1, then E(Xn) Converges to E(X). Give an example to show that the converse is false