The series Ʃ ((n!)^n) /(4^(4n)) is determined to be divergent using the root test. The application of the root test simplifies the expression to (n!)/n^4. Upon taking the limit, the result approaches infinity, confirming the divergence of the original series. It is crucial to note that the nth root of 4^(4n) is not n^4, which is a common misconception in the analysis.
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Jbreezy said:Homework Statement
Ʃ ((n!)^n) /(4^(4n))
Homework Equations
Root test?
The Attempt at a Solution
Can you do ... the root test so then you will get rid of exponents n and you have
(n!)/n^4 then take the limit and you get ∞ so the original sum is divergent?