Weierstrass starts with the terms of a series 0<a_n<1 and continues to prove that the product of the terms (1-a_n) lies between certain limits. When n=1, a_n is a1, so S1=a1 and 1-S1=1-a1. From there the proof goes on to expand the agument by induction and finally provide proof. So your question is asking why the inequality is there, when in actual fact the inequality is the premise from which the theorem is based. In other words, we start with the assumption that each term is between 0 and 1, rather than proving that it is. If you go over the pages you sent me, you will see the whole theorem laid out with its proof. If there's any part you need to understand better, please let me know.