# How do you use the Root Test on the series #sum_(n=1)^oo((n!)/n)^n# ?

By Root Test,

Let us look at some details.

Consider:

#lim_{n to infty}rootn{|a_n|}=lim_{n to infty}rootn{[(n-1)!]^n} =lim_{n to infty}(n-1)! =infty#,

which is greater than 1; therefore, we can conclude that the series diverges by Root Test.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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