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[(n+2)!/(n+1)^(n+2)] /型察纯 [ (n+1)!/n^(n+1) ]
=[(n+2)!/(n+1)! ] .[ n^(n+1) /(n+1)^(n+2)]
= (n+2) . [ n^(n+1) /(n+1)^(n+2)]
=[(n+2)/(n+1)] .[ n^(n+1) /(n+1)^(n+1)]
=[(n+2)/(n+1)]. [ n/(n+1) ]^(n+1)
= [(n+2)/(n+1)] .[ 1- 1/(n+1) ]^(n+1)
lim(n->没凳∞) { [(n+2)!/(n+1)^(n+2)] / [ (n+1)!/n^(n+1) ] }
=lim(n->∞) [(n+2)/(n+1)] .[ 1- 1/(n+1) ]^(n+1)
=lim(n->∞) [(n+2)/(n+1)] .lim(n->∞卜咐)[ 1- 1/(n+1) ]^(n+1)
=e^(-1)
=[(n+2)!/(n+1)! ] .[ n^(n+1) /(n+1)^(n+2)]
= (n+2) . [ n^(n+1) /(n+1)^(n+2)]
=[(n+2)/(n+1)] .[ n^(n+1) /(n+1)^(n+1)]
=[(n+2)/(n+1)]. [ n/(n+1) ]^(n+1)
= [(n+2)/(n+1)] .[ 1- 1/(n+1) ]^(n+1)
lim(n->没凳∞) { [(n+2)!/(n+1)^(n+2)] / [ (n+1)!/n^(n+1) ] }
=lim(n->∞) [(n+2)/(n+1)] .[ 1- 1/(n+1) ]^(n+1)
=lim(n->∞) [(n+2)/(n+1)] .lim(n->∞卜咐)[ 1- 1/(n+1) ]^(n+1)
=e^(-1)
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