Prove that 1+3+5+...+(2n 1) = n? for any integer n > 1. Proof by Induction: Base Case: (n = 1) ES=1 RS= M7 Thus the base case holds form = 1. Inductive Hypothesis: Suppose 1+ 3+ 5+...+(2n 1) = n?is true for some n k > 1, that is, we assume that f= ~ Inductive Step: Prove that 1 + 3+ 5+...+(2n 1)= n? is true for n = & + 1, that is, we need to show that We have that v= w (using the inductive hypothesis). And this simplifies to wo. Therefore, by the principle of mathematical induction,1 + 3 + 5+...+(2n1) = n? for any integer n > 1. Q.E.D. A.1+345+...4+(2k-1)4+2k 614+3454+...4+(2(k+1)+ 1) 1+34+5+...+(2k-1) B. (k +1)? FR 1 C.k(k +1) + (2k +1) G. 2? K. k? + (2k +1) D.1+3+5+...+(2k1)+(2k+1) H. k? + (2k 1) L.1+ (2(1) 1)