I have this question and I think i've done it. The trouble is, thinking i've done it isn't enough and I need to know if I actually have!

Question: Use induction to prove that if both x and y are positive then .

I did this:

I rearranged it like so

For n=1:

Therefore it is true for n=1.

For n=k:

For n=k+1:

We know that and so this inequality makes sense.

At this point I think it has been proven true for n=k+1.

So is that the end of the proof? I still have to write the little thing on the end explaining it was proof by induction. I just want to know if this is the right method.