1. The problem statement, all variables and given/known data By choosing the correct vector b in the Schwarz inequality, prove that (a1 + ... + an)^2 =< n(a1^2 + ... +an^2) 2. Relevant equations Schwarz inequality 3. The attempt at a solution since the answer key says that a1 = a2 = ... = an, i tried plugging in values, but i am not getting anywhere and i completely have no intuition of what is happening here. and while on the topic, can anyone recommend books to read - both introductory and more advanced ones about inequalities? i would like a book that gives visual and geometric intuitions. books with proofs would be nice, but it's not a priority to me just yet. thank you!