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#1 2016-09-22 06:45:19

markosheehan
Member
Registered: 2016-06-15
Posts: 51

induction

prove by induction that 2^n is greater than or equal to 1+n when n are natural numbers. i tried subbing in k+1 in for n but i get stuck

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#2 2016-09-22 07:56:28

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: induction

Suppose it is true that
Notice that
What can you do from here?

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#3 2016-09-23 03:54:23

markosheehan
Member
Registered: 2016-06-15
Posts: 51

Re: induction

sorry i do not know to work it out from here i tried factorising but didnt get anywhere

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#4 2016-09-23 07:53:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: induction

Hi;

I would try this:

Prove the base case of n = 1 and n = 2

Let us assume what we want to prove is true

then

A) says if

is true then that implies that
is also true.

Now we go to the n + 1 step

It is very easy to prove that

when n > 2 and
so we have proved that if A) is true so is B) and we are done.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2016-09-23 08:34:27

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: induction

markosheehan wrote:

sorry i do not know to work it out from here i tried factorising but didnt get anywhere

Note that the
sign would acually be
if you included 0 in your definition of natural numbers.

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