9231 Further Mathematics:
General structure for proof by
mathematical induction:
0. (for divisibility) Let f(n) = given equation.
1. Write your opening inductive statement:
Let P_k be the statement that, for some value n= k, your expression is true. State
the given restriction for n (e.g: for all positive integers n)
2. For P_1: n=1: ……..
therefore, P_1 is true.
3. When n=k+1, …
For divisibility proofs:
When n=k+1, consider : f(k+1)=f(k)
f(k+1)-f(k) = …
4. Hence, P_k ⇒ P_k+1.
5. Hence, since P_1 is true and P_k ⇒ P_k+1, by mathematical induction, P_n is
true for… (write the given restriction for n).
9231 Further Mathematics: General structure for proof by mathematical induction:
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