Only questions 2, 4, 6, 8,

In Exercises I through 7, prove the statement is true by using 8. Let P(n): 13 + 23 + 33 + ... + n3 n2 (n + 1)2 + 4 mathematical induction. 4 1. 2+4+6+ . . . + 2n = n(n + 1) (a) Use P(k) to show P(k + 1). (b) Is P(n) true for all n 2 1? 2. 12 + 32 + 52 + ... + ( 2n - 1)2 _ 1(2n + 1) (2n - 1) 9. Let P(n): 1 + 5 +9+ . . . + (4n - 3) = (2n + 1)(n - 1). 3 (a) Use P(k) to show P(k + 1). 3. 1 + 2' + 22 + ... + 2" = 20+1 - 1 (b) Is P(n) true for all n > 1? 4. 5 + 10 + 15 + . . . + 5n = 5n(n + 1) 10. Prove 1 + 2" 2. 2 11. Proven 1. 5. 12 + 22 + 32 + ... + 12 - 1 n(n + 1)(2n + 1) (2n + 1)2 6 12. Prove 1 + 2+ 3 + ... +n