# `a_n=cos(2/n)` Find the limit (if possible) of the sequence.

`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...

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`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.

Approved by eNotes Editorial Team