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Write the value of lim(n->oo)(n !+(n+1)!...

Write the value of `lim_(n->oo)(n !+(n+1)!)/((n+1)!+(n+2)!)`

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`lim_(n->oo)(n !+(n+1)!)/((n+1)!+(n+2)!)`
`lim_(n->oo)(n !+(n+1)n!)/((n+1)!+(n+2)(n+1)!)`
`=lim_(n->oo)(n!(1+n+1))/((n+1)!(1+n+2))`
`=lim_(n->oo)(n !(n+2))/((n+1)n!(n+3))`
`=lim_(n->oo)(n+2)/((n+1)(n+3))`
`=lim_(n->oo)(+2/n)/(n(1+1/n)(1+3/n))`
`=0`
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