# ~~~inequality-- hard

• Aug 7th 2006, 11:03 PM
fring
MATHEMATICAL INDUCTION~~~inequality-- hard
hey guys!! can anyone help me with this hard question?
its to do with mathematical induction (inequalitites)
i think im missing a step in my proof and i just cant figure it out....

heres the question:

Prove that 2^n>3n for all positive integers where n is greater than or equal to 4

thanks guys
any help would be great
• Aug 7th 2006, 11:56 PM
earboth
Quote:

Originally Posted by fring
hey guys!! can anyone help me with this hard question?
its to do with mathematical induction (inequalitites)
i think im missing a step in my proof and i just cant figure it out....
heres the question:
Prove that 2^n>3n for all positive integers where n is greater than or equal to 4

thanks guys
any help would be great

Hello, fring,

I presume, that you know, that this proof has to be done in 3 steps:

1. 2^4 > 3*4 is true

2. ***ume that 2^n > 3*n for all n greater than 4

3. Proof (under ***umption step 2) that
$2^{n+1}>3(n+1)$
$2^n*2>3n+3$
$2^n+2^n>3n+3$

Compare both sides of this inequality: 2^n >3n according to ***umtion (step 2). Because 2^n > 3 for all n greater than 4 the last inequality is true for all n.

Greetings

EB

PS: The writing with 3 stars was not done by me. Someone in this forum had set a filter to avoid all disgusting words. Kind of funny!