Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 24

a_n=cos(2/n)
To determine the limit of this function, let n approach infinity.
lim_(n->oo) a_n
=lim_(n-> oo) cos(2/n)
To solve, let the angle 2/n be equal to u, u = 2/n .
Take the limit of this angle as n approaches infinity.

lim_(n->oo) u = lim_(n->oo) 2/n = 0

Then, take the limit of the cosine as u approaches zero.

lim_(u->0) cos(u) = cos(0) = 1

So the limit of cos(2/n) as n approaches infinity is equal to 1.
lim_(n->oo) cos (2/n) = 1

Therefore, the limit of the given sequence is 1.