Math Is Fun Forum

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Induction Help Please

Prove that 1 + 2^n ≤ 3^n for n≥1.

Basis Step: n(1) is true 3<=3.
Inductive Step: I don't even know how to start this.. Except that you have to prove P(n+1) i think..

Last edited by panthersoccer (2011-12-12 11:13:59)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Induction Help Please

hi panthersoccer

start with

Now  show that is less than or equal to

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Re: Induction Help Please

I get how you got that far. You just manipulated the numbers to get like that. But how do you know that you want it to look like that? And then how do you connect it to the other side of the inequality?

Like this?

Last edited by panthersoccer (2011-12-12 11:57:29)

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Re: Induction Help Please

Or do you show it like this:

Last edited by panthersoccer (2011-12-12 12:59:10)

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Re: Induction Help Please

Please help... I'm so frustrated

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Induction Help Please

hi panthersoccer

Sorry if you felt I was ignoring you.  I'm in the UK so I've been asleep.  It was nearly midnight when I last posted and it's 0727 GMT now.

I got to:

Now we know that we are allowed to assume

and what we want to show that

So I wrote the left hand side of this and tried to make it look like what we are assuming so I could use that.

but

So if we subtract another 1 from the left hand side

which is what we need.

In fact I think the 'less than or equal' can be a strict 'less than'.  But either way, it's the induction step done.

Hope that helps, 

Bob

Last edited by Bob (2011-12-12 19:47:37)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Re: Induction Help Please

Oh see i thought I needed

Last edited by panthersoccer (2011-12-13 00:26:43)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Induction Help Please

hi

Well that's what I've posted.

My proof is in two parts; the part I posted yesterday and the part I did today.

You'll need to string them together.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

panthersoccer

Member

Registered: 2011-12-12

Posts: 6

Re: Induction Help Please

Yeah sorry its early I get what you're saying. Thank you so much.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Induction Help Please

Oh good.  I was hoping you would.

Are you in the States?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob