Proof by induction that

K+1 Step

Then im stuck here....

Any help would be appreciated.

Thanks in advance

Printable View

- February 15th 2010, 09:10 AMfirebioProof by Induction : Inequalities
Proof by induction that

K+1 Step

Then im stuck here....

Any help would be appreciated.

Thanks in advance - February 15th 2010, 11:43 AMNyrox
You left out a term in the last line. It should read

What you need to show now is that:

,

or equivalently, that

.

Squaring both sides (both sides are positive, as ) we get

.

I'll let you conclude :) - February 15th 2010, 12:06 PMfirebio
Thanks for help

I think i get it

so

Then

That means

Finally

So - February 16th 2010, 03:35 AMHallsofIvy
"so "? There was no "K" in what you did before. If you mean "k", that is not what you were trying to prove and there is no need to say it- since "k" was in N, certainly k+1 is.

Your last line should be "so the statement is true for all n". - February 16th 2010, 04:59 AMArchie Meade
There is no need to bring in

Therefore, the following should be true

We try to prove this using the first statement, since that will link every pair of adjacent natural numbers in a chain.

Is ?

?

?

?

Yes.

The adjacent-term chain is established.

Finally prove the inequality is true for an initial value of n.

__Then__it's true for that n and all following n.