Determine Divergence of Ʃ ((n!)^n) /(4^(4n))

[Jbreezy]

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?

 

[Dick]

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?

Yes, you use the root test. But the nth root of 4^(4n) isn't n^4.