How do you find the nth root of n!?

Ethen Wong

Ethen Wong

Answered question

2022-01-30

How do you find the nth root of n!?

Answer & Explanation

Lily Thornton

Lily Thornton

Beginner2022-01-31Added 19 answers

The precise value requires you to calculate n! using the recursive definition:
{0!=1n!=n(n1)!
then take the n-th root.
However, note that a good approximation to n! is given by the Stirling series:
n!2πn(ne)n(1+112n+1288n213951840n3+O(n4))
Then:
(n!)1n(2πn)12n(ne)(1+112n+1288n213951840n3)1n
This will be good for about 10 significant digits.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?