How Many Solutions??

Algebra Level 3

How many positive integers $n$ are there that satisfy the following:

$\large 1!+2!+3!+4!+n!\le n^3$

1 0 2 3 Infinity of solutions

1 solution

X X
Jul 31, 2018

$n^3>33$ ,so $n$ at least has to be $4$ .

$n!<n^3$ ,so $n$ cannot be bigger than $5$ .

By checking,only $n=4$ fits.

Actually there are four integers 1,2,3=4

A Former Brilliant Member - 2 years, 5 months ago