Data Structures and Algorithm Analysis in C - SVS

Structures, Algorithm Analysis: CHAPTER 1: INTRODUCTION
< (3/5)(5/3) k+1 + (9/25)(5/3) k+1
which simplifies to
F k+1 < (3/5 + 9/25)(5/3) k+1
< (24/25)(5/3) k+1
< (5/3) k+1
proving the theorem.
As a second example, we establish the following theorem.
THEOREM 1.3.
PROOF:
The proof is by induction. For the basis, it is readily seen that the theorem is true when n = 1.
For the inductive hypothesis, assume that the theorem is true for 1 k n. We will
establish that, under this assumption, the theorem is true for n + 1. We have
Applying the inductive hypothesis, we obtain
Thus,
proving the theorem.
Proof by Counterexample
mk:@MSITStore:K:\Data.Structures.and.Algorithm.Analysis.in.C.chm::/...
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2006-1-27