He wants to match the index of summations, to make them all start from n = 2.The the first one starts from n =2, so leave that; the second one and the fourth one start from n = 0, so write down the first two terms of each; and, finally, the third one starts from n =1, so write down its first term. That's basically where your expression came from (check it). It seems to me, though, in the next two latex lines, he had forgotten that he had matched the index of the summations. In any case, websites aren't that good a source of learning -- it's far better to learn from a book, in my opinion.