Question 1: True or False? Justify your answers. (1) For each n2 : (n1)2=(n2)+(n+12) (2) Let k and r be two integers with 1rk. If (k+1r) and (kr) are even, then (kr1) is odd. (3) (2kk)=2(2k1k) for each k1. (4) In Pascal's triangle, if we sum all numbers in any row (except the first row) we will get an even number. Question 2: Prove by mathematical induction on n that (rr)+(r+1r)++(nr)=(n+1r+1) for all positive integers n and r satisfying 0rn. Question 3: Let n be a positive integer and r be an integer satisfying 1rn. (I) Prove that r(nr)=(n+1r)(nr1) (II) Use part (I) to show that (nr)>(nr1)ifandonlyifr(nr1)ifandonlyifr