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underset n rarr oo Lt((n!)/(n^(n)))^((1)...

underset n rarr oo Lt((n!)/(n^(n)))^((1)/(n))=

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lim_ (n rarr oo) [(n!) / (n ^ (n))] ^ ((1) / (n))

Evaluate : underset(n to oo)lim(n)/((n!)^((1)/(n)))

{:(" "Lt),(n rarr oo):} ((n!)/(n^(n)))^(1/n)=

{:(" "Lt),(n rarr oo):}(((2n)!)/(n!n^(n)))^(1/n)=

lim_(n rarr oo) (4^(n)+5^(n))^(1/n) =

lim_(n rarr oo) (4^(n)+5^(n))^(1/n) =

lim_ (n rarr oo) (n) / ((n!) ^ ((1) / (n)))

lim_(n rarr oo) (4^(n)+5^(n))^(1/n) =

Lt_(n rarr oo)(1+(1)/(n))^(n)