SOLUTION: show that if n is an integer greater than 3, n!>2^n.

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Question 29414: show that if n is an integer greater than 3, n2^n.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
show that if n is an integer greater than 3, n2^n.
WE HAVE FOR N=4
4!=1*2*3*4=24 >2^4=16...IS OK...SO....
FOR N>3 WE HAVE
N!=(1*2*3*4)*(5*6*7..........N)
>(2^4)*(2*2*2*...........2...(N-4) TIMES)=2^4*2^(N-4)=2^(4+N-4)=2^N...
HENCE N2^N