For which nonnegative integers n is n^2\leq n!?

sjeikdom0

sjeikdom0

Answered question

2021-05-19

For which nonnegative integers n is
n2n!?

Answer & Explanation

aprovard

aprovard

Skilled2021-05-20Added 94 answers

Let us determine the possible integers for which n2n! by constructing a graph of the two functions f(x)=x2 and g(x)=x!
The two graphs are then intersected (3.5624, 12.6906). For values n larger than 3.5624, the inequality n2n! will then hold.
Given that n is an integer:
n>3
Moreover, we note that the equality holds for n=0 and n=1 as well, since 0!=10=02 and 1!=1=12

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?