Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 22

a_n=6+2/n^2
To find the limit of a sequence, let n approach infinity.
lim_(n->oo) a_n
=lim_(n->oo) (6 + 2/n^2)
=lim_(n->oo) 6 + lim_(n->oo) 2/n^2
Take note that a limit of a constant is equal to itself lim_(x->c) a = a.
Also, if a function is in the form a/x^m , where m is any positive number, its limit as x approaches infinity is zero lim_(x->oo) a/x^m =0
lim_(n->oo) 6 + lim_(n->oo) 2/n^2
= 6 + 0
=6
Therefore, the sequence's limit is 6.