Question

I really need help! Please! I'm doing mathematical induction but I have no idea what is going on!
The questions says: For the given statement P(small n), write the statements P(little 1), P(little k), and P(little k + 1). 2 + 4 + 6 + ... + 2n = n(n + 1)

Answer 1

In mathematical induction we show that P(1) is true by merely putting the value.
In next step we assume P(n) is true and using that we show that P(n+1) is true and that is all about Mathematical induction.

Answer 2

I understand how to do the first one, but after that I don't understand it. Could you show me how to do it?

Answer 3

In the induction process first you prove that both sides are equal for P(1)

so,
P(1)
----
2=1(1+1)
2=2
L.H.S=R.HS

Now let's assume that this is true for n=k.
2 + 4 + 6 + ... + 2k = k(k + 1) -(1)

Now comes the inductive step in play.if we have to prove for n=k+1 the ultimate expression which we should end up should be:
2 + 4 + 6 + ... + 2(k+1) = (k+1)(k + 2) -(2)


So now to prove it we will add k+1 in eqn(1) and try to prove it by making it equal to eqn(2)

Answer 4

I hope you got it? :|

Answer 5

That helped a little, but I still don't understand where the k comes from and it confuses me when it's thrown in... :(

Answer 6

Well we just replace n with a k.Because we are assuming that n is equal to k,so we can prove n is equal to k+1 that would be our inductive step.

To understand this consider a number of domino lined up together in such a way that you hit one and all the others lined up will also go down.If you try to drop the 1st one,the 2nd one will also fall and the 3rd one too. So if n=2 and if n is true then n=3 should also be true.

I'm not very sure about this but i hope this helps

Answer 7

Uhm it seems like it might make a little more sense... Thanks for trying. I'm just really having trouble with these concepts, and how they work out.