3,4,5

3. Consider the sum (3)2 + (8)2 + (13)2 + . . . + (15n - 2)2: (a) Write the sum in sigma notation. m m (b) Use identities Ck = [m(m+1)] and [m(m + 1)(2m + 1)] to prove that k= 1 (3) 2 + (8)2 + (13) 2 + ... + (15n - 2)2 = =(n) (450n2 + 69n - 35). 2n 4. Prove that ) (((+ 1) = [n(n + 1)(2n + 1)] by each of the following two methods: e = 1 (a) By mathematical induction on positive integer n 2 1. (b) By using the identities mentioned in part (b) of question 3 5. Evaluate 91 + (-2)914 -2+ V3i 290 2 , where z - -V3 + 2. Simplify as much as possible. i