Whenever someone has a moment, can you answer this? It is the very first example in the book: http://i.imgur.com/lxbdp.jpg
(I underlined the part in red in the picture)
This is the only part I couldn't understand right from the beginning.
In the inductive step, when they are writing the formula for P(k+1), how did they get it?
On the right side all clear - they replaced k with k+1 as I would expect.
But on the left side there's still k and they added (k+1)? I don't get that.
Why didn't they replace k with k+1, like they did on the right side?