# Questions about Infinite Sequence....? Determine whether the following sequence converges or diverges. If it converges, then find its limit? Sequence is: 2^n/(2n)! Plz explain me with step by step...! Plz tell me as soon as possible...!

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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