Also, I'd expect to see the word "all" somewhere in this first paragraph -- I think it's worth emphasizing the point that if we have the base case and the inductive step then the statement will be true for all of the numbers after the base case, just like all of the dominoes after the first one would fall down. I think the current final sentence of the intro paragraph doesn't make this clear enough.
I think it would be worthwhile to explicitly call out that what's happening here is that we're replacing n in the original equation with k+1.
I really like this domino analogy.
Also, I'd expect to see the word "all" somewhere in this first paragraph -- I think it's worth emphasizing the point that if we have the base case and the inductive step then the statement will be true for all of the numbers after the base case, just like all of the dominoes after the first one would fall down. I think the current final sentence of the intro paragraph doesn't make this clear enough.