Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 147 — #155
5.3. Strong Induction vs. Induction vs. Well Ordering 147
Figure 5.12 S 0 ; S 1 ; S 2 and S 3 .
Exam Problems
Problem 5.14.
Prove by induction that
nX
k kŠ D .n C 1/Š 1: (5.16)
1
Problem 5.15.
Prove by induction:
n.n C 1/ 2
0 3 C 1 3 C 2 3 C C n 3 D
; 8n 0:
2
using the equation itself as the induction hypothesis P.n/.
(a) Prove the
base case .n D 0/.
(b) Now prove the
inductive step.