SE 500 Mathematics for Software Engineering
Fall 2022
HW #10 (preliminary edition)
Due: 4:00pm, Friday, December 2
1. Prove by (weak) mathematical induction that
(+i | 1≤i≤n : 2i + 5) = n2 + 6n
for all n ≥ 0.
2.
Define f : ℕ → ℕ as follows:
| f.0 | = | 1 |
| f.1 | = | 2 |
| f.n | = |
3·f(n-1) - 2·f(n-2) (for n≥2) |
Prove by (strong) mathematical induction that f.n = 2n
for all n ≥ 0.