# Series tests containing n!

Discussion in 'Other Advanced Math' started by oasisinau, Jul 31, 2024 at 11:55 AM.

1. ### oasisinau

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I have a query about n! in various root, ratio etc tests for convergence.

Consider f^n(x^n)=n!
I have that 3 different n’s in this equation are:
- n in f^n as an indicator of order
- n in x^n as the exponent or degree of the variable x
- n! as factorial n, ie any integer

My question is why n! Is not considered to be a constant and (as such) moved to the left of summation in all series tests

Thanks
Owen

oasisinau, Jul 31, 2024 at 11:55 AM
2. ### Phrzby Phil

Joined:
Mar 8, 2022
Messages:
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I'm not sure what you're proposing or asking here, so I've waited for anyone else to chime in.
That not having happened, please clarify.

There is no summation in the equation, so I don't get the question.

Are you proposing there is a functional expression for f meeting these criteria?

Taking some values for n:
f(x) = 1
f^2(x^2) = 2
f^3(x^3) = 6
etc.

Is this where you're going?

Thanks.

Phrzby Phil, Aug 1, 2024 at 10:43 PM
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