prove it-good one

JEE Mains 2015 Forum › Algebra questions › prove it-good one

prove that
(n!)² > nⁿ

(i know the proof but am looking for a much simpler one)

#Mathematics #Algebra

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7 Answers

39

Dr.House ·2009-10-15 10:53:45

first tell me what proof u know?

and do u know higher algebra?

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1

Arshad ~Died~ ·2009-10-15 10:59:01

i know the proof by rearrangement of the factors in (n!)²

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39

Dr.House ·2009-10-15 11:12:20

ok, so r u into higher algebra?

my proof involves some wat higher algebra, not simple math..

thats why asking..
anwyays will work out something else by a simpler method.. now got to go

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1

Arshad ~Died~ ·2009-10-15 11:13:09

pls do try...!!
i will be very happy to see something simple
:-)

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Arshad ~Died~ ·2009-10-18 03:34:23

anyone..........plz!!

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62

Lokesh Verma ·2009-10-18 03:59:06

I guess I have a proof...

n! > n . (n/2) . (n/3) ... (n/n-1) . n/n

now you can simply use

n>=n
n-1 > n/2
n-2> n/3

1>=1

All these will hold if n>1, 2, 3, .. n-1 respectively...

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Arshad ~Died~ ·2009-10-18 04:06:17

thank u so much sir......

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Your Answer

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