please help with limit proof
I have a 3 parter. I think I have the first part, the second part I am not sure of and the third part I am kind of getting desperate with...
(a) Prove first that if c is a constant, and , then .
(b) Prove that if then . (Hint:recall that convergent sequences are bounded.)
(c) Use the polarization identity to prove that if and , then .
(a) Since for all , there exists an , such that if , there should
exist an such that hence
(b) implies that is compact and bounded. Take . For some , if , then and therefore . so now .
Take which gives us
(c) If my other two are even correct, this is where I am stuck. PLEASE give me a little nudge...