1. Let (an)? and (bn). 21 be bounded real sequences and let (Cn). 1 be the sequence a1, b1, @2, 62, . . Prove that lim sup Cn lt; max(lim sup an,

Please help me solve the following concerning limsup and liminf of sequences.

1. Let (an)?and (bn).21 be bounded real sequences and let (Cn).1 be thesequencea1, b1, @2, 62, . .Prove thatlim sup Cn < max(lim sup an, lim sup bn)n-toon-toon-tooand that if (an) 1 and (bn)?-1 converge to y then so does (Cn)?21.