Discrete Math Questions

5. Prove by mathematical induction: Ci(i+ 1)(2+2) _ n(n + 1)(n+ 2)(n+3) 1=1 4 for all integers n 2 1. 6. Consider the following statement: n II(1 + 2 27) _1-22+1 T=1 1- 72 for all integers n 2 1 and any real number z * +1. (a) Prove the basis step of a proof by mathematical induction of the statment. [Hint: (1 - x4) = (1+x2)(1 -x2).] (b) State the induction hypothesis for the induction step of a proof of the statement. DO NOT PROVE the induction step. 7. Prove by contraposition: "If n is an integer and n is odd, then n + 1 is even." PART II: Select ONE of the following two problems to work. If you submit answers for both then only Problem #8.A. will be graded - so don't submit both! 8.A. Prove this statement: "Va, b, c E Z, if alb and blc then a2|(62 -c2)."