Math Is Fun Forum

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

zetafunc

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Registered: 2014-05-21

Posts: 2,436

Website

Re: induction

Suppose it is true that

Notice that

What can you do from here?

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

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.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: induction

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.