Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

acceptable proof?

Is this an acceptable proof? I have a feeling it is flawed somehow.

Let

. Prove that:

For n = 1, we have

, which is true.

We make the assumption that:

for

Taking n = k,

Multiplying both sides by k+1,

Since

, we can divide them out and we are left with

, which is true.

Thus the proposition is true, QED

Last edited by Identity (2007-12-15 16:27:24)

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: acceptable proof?

You are forgetting that you must show

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: acceptable proof?

Yep, it looks like you tried to prove the induction step backwards.  You started with an assumption for k and tried to move forward to the k+1 step.  You're supposed to start with the k+1 step and then work your way backwards until you can use your assumption for k to prove your inequality.  What you need to do is take what Ricky posted and simplify it until you can use your assumption of k to prove the induction.

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Wrap it in bacon

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: acceptable proof?

Last edited by JaneFairfax (2007-12-17 03:10:47)