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Basically, you have to prove something on the LHS is equal to something on the RHS by induction. So you first show that it's true for a base case (ie n=1) then generalise this to n=k, and then you assume that the equation holds at n=k. Then the next thing to do is that you show that the equation still holds for n=k+1, and so you either add the term to both sides or you multiply both sides by whatever term it is. This is the bit that confuses me, because I think all you have to do is show that now the LHS still equals the RHS, but of course it does, if you take 2 equal things and multiply them by the same number, then of course they will still be equal? I think maybe where I'm going wrong is that, the end result on the RHS will look the same as the RHS for n=k, except it will be k+1 and this shows that it's true. But it don't really get this, I'm not sure why it is that you can't just assume it's going to be true for n=k+1?

I know there's something obvious that I'm not seeing, I just can't get there.

Thanks