I have to find the limit superior and the limit inferior of these sequences:

a)

n + [(-1)^n](2n+1)

---------------- It appears limsup = 3 and liminf = -1.

n

b)

(an)^(1/n) where an = 1/(2^[(n+1)/2]) if n is odd and 1/(3^(n/2)) if n is even. What are the limsup and liminf of these? They seem less obvious.

Thanks in advance for any help.