Consider the sequences:
(1) aₙ = (-1)ⁿ + 1/n
(2) aₙ = (-2)(-n)
(3) aₙ = 4 + n

Find limsup aₙ and a subsequence converging to it.

a) limsup aₙ = 5, subsequence: a₂, a₄, a₆, ...
b) limsup aₙ = 4, subsequence: a₃, a₅, a₇, ...
c) limsup aₙ = 4, subsequence: a₁, a₃, a₅, ...
d) None of the above