11I think this is what u intended....
n!<{n+12}^n....
106If that is the case
then:
n!=(1*n)(2*(n-1))*.....
(1+n)2/4 ≥ 1*n
(2+n-1)2/4 ≥ 2*(n-1)
.
.
.
continuing and multiplying
(n+12)2(n/2) ≥ n!
or n! ≤ (n+12)n
1@asish correct solution.
but equality is not valid.
keep trying there's a simpler solution
1
rahul1993 Duggal
·2009-08-13 02:36:14
oh i forgot to mention n>1 asish your solution is perfect
106
Asish Mahapatra
·2009-08-13 02:36:29
yeah equality not valid bcz nos are not equal... :)
11
Devil
·2009-08-13 08:34:23
What abt AM-GM on 1st 'n' naturals?