Mathematical Induction (MI) is a method to prove statements that cannot be demonstrated readily by a direct argument. This proving technique can be compared to the process of making dominoes fail. If we can
(i) make the 1st domino fall and
(ii) show that if the k-th domino falls then the (k+1)-th domino will fall,
we can conclude that all dominoes will fall.
We can use this method to prove statements on series and sequences.
This topic is new to all JC1 H2 Maths students so I’ve prepared a Mathematical Induction Template Summary to provide students the framework for them to present their steps systematically.
You can save the Template Summary using “Right-click, Save as” or your mobile phone can “Save Image As”. With that you can refer to the template summary anytime you are working on your tutorial questions.
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H2 Maths – Mathematical Induction Template Summary
Prove by induction for ,
Step 1: Write down the proposition
Example: Let P(n) be the proposition for
Step 2: Verify the proposition with the smallest value of n
LHS of P(2) =
RHS of P(2) = = LHS of P(2)
Therefore P(2) is true.
Step 3: Assume P(k) is true for some positive integer k
Assume P(k) is true for some ,
Step 4: Use the above assumption to prove is true
Example: We want to show that P(k + 1) is true i.e
LHS of P(k + 1)
RHS of P(k + 1)
Step 5: State the conclusion
Since P(2) is true and P(k) is true P(k + 1) is true.
By mathematical induction, the proposition P(n) is true for all , .