*Determine whether the following sequence converges or diverges. If it converges, then find its limit?** Sequence is: 2^n/(2n)!*

We apply the ratio test: consider the following limit

`lim_(x -> oo) (a_(n+1))/(a_n)` where `a_n=(2^n)/((2n)!)` * *

`lim_(n->oo)[(2^(n+1))/((2(n+1))!)-:(2^n)/((2n)!)]`

`=lim_(n->oo)[(2^(n+1))/((2n+2)!)*((2n)!)/(2^n)]`

`=lim_(n->oo)[2/((2n+2)(2n+1))]`

=0.

Thus the sequence converges to 0.

* *

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