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...!  

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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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