Suppose the sequence {a_n} converges to L and limsup{b_n} = M < infiniti

//({b_n} is bounded below and above)// Prove limsup{a_n*b_n} = LM.

b) also show that the statement is false if {b_n} is not bounded below.

My Sketch: I have to show that limsup{a_n*b_n} = Q is finite; then use

subsequences to show Q less than or equal to LM, and that is greater than or equal to LM.