We substitute n=1 



That's true.

Assume true for n=k

(1)  

We want to show that if (1) is true, then the following is true:

     

which simplifies to this:

(2)  

----------------------------------------------

So we start with what we assume to be true, which is (1):



and add the next term  to both sides:



Now if we can show that the right side



is equal to the right side of (2) then we will have proved the
proposition by induction:

 =

We get an LCD of (k+1)(k+2)

 =

 =

 =

 =

 =



That's the same as the right side of (2) above.  So we are done.

Edwin