1. Use induction to prove that Summation with n terms where i=1and Summation 3i 2 ? 3i + 1 = n^3 for all n ? 1.
2. Let X be the set of all natural numbers x with the propertythat x = 4a + 13b for some natural numbers a and b. For example, 30? X since 30 = 4(1) + 13(2), but 5 ?/ X since there’s no way to add4’s and 13’s together to reach 5. (It’s not a multiple of 4, andadding 13 goes over.) Use strong induction to prove that n ? X forall integers n ? 36. Hint: it should be easy to show that k + 1 ? Xif k ? 3 ? X. You may need multiple base cases for this problem
