Need help with Mathematical induction question?

I'm working on a problem and I'm not sure I have this correct on how to do it.

here is the problem

Prove the following statement by mathematical induction:

1/2+1/6+...+1/n(n+1)=n/n+1, for all integers n> or = 1

My first thought is to solve the n/n+1 side with the number 1

So I get 1/2 on both sides by substituting. Then I start to become unsure on where to go from there.

Any help would be awesome.

Re: Need help with Mathematical induction question?

First show the base case is true:

True.

State the induction hypothesis :

Add to this the equation:

Simplify by incorporating the added term within the summation on the left and combining terms on the right, and you will find you have derived from , thereby completing the proof by induction.

Re: Need help with Mathematical induction question?

Induction is not necessary.

Re: Need help with Mathematical induction question?

Mark, awesome answer, but a quick question I thought you had to go prove it in terms of K+1. Although I've been wrong before, thanks a bunch.

Re: Need help with Mathematical induction question?

If you carry out the operations I suggested you will get:

This is , which was derived from .

Re: Need help with Mathematical induction question?

Wait, so how did we get 1/(n+1)((n+1)+1) = n+1/n+2 sorry for drawing this question out just trying to understand the different parts.

Re: Need help with Mathematical induction question?

State the induction hypothesis :

Add to this the equation:

On the left we may incorporate the added term within the summation:

On the right combine terms:

Now we have , completing the proof by induction.