`a_n = 6+2/n^2` Find the limit (if possible) of the sequence.

`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.

Comments

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