### Real Analysis lim sup and lim inf

Let {a_n} and {b_n} be sequences in [-infinity,+infinity] and prove the following assertions: 1). a).Lim sup (as n -> infinity) ( a_n + b_n) less than or equal to lim sup a_n + lim sup b_n ( as n foes to infinity). b).Show by an example that strict inequality can hold. Provided none of the sums is of the form infin