Prove that the following is true for all positive integers
n
by using the Principle of Mathematical Induction: Theorem:
f(n)=2+3n
is a solution to
f(n)=f(n−1)+3
where
f(0)=2
Conjecture
∀nP(n)P(n)≡f(n)=2+3n
Inventory: - Base Step:
P(0)=f(0)=2+3(0)
- Inductive Hypothesis:
P(k)=f(k)=2+3(k)
. - Inductive Conclusion:
P(k+l)≡f(k+1)=2+3(k+1)