Mathematical induction checklist: Steps to a perfect H2 Math proof

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The base case is the initial value (usually n=0 or n=1) for which you directly prove the statement is true. Its crucial because it establishes the foundation upon which the inductive step builds. Without a valid base case, the entire proof collapses, regardless of how strong your inductive step may seem. For H2 Math, a clearly demonstrated and correct base case is a key component of a complete and convincing proof, earning crucial marks.
The inductive hypothesis is the assumption that the statement youre trying to prove is true for some arbitrary integer k (where k ≥ base case). You explicitly state, Assume the statement is true for n=k. This assumption is the cornerstone of your inductive step, allowing you to build a logical bridge to prove the statements validity for the next integer, k+1. Without a correctly stated inductive hypothesis, your proof is incomplete.
The most common mistake is failing to clearly show how the assumption for n=k directly leads to the conclusion for n=k+1. Students often present algebraic manipulations without explicitly demonstrating the connection between the two. A strong inductive step must clearly utilize the inductive hypothesis to transform the expression for n=k+1 into a form that validates the original statement. Missing this logical link is a frequent cause of lost marks.
You must explicitly state a conclusion that summarizes your findings. A typical concluding statement is: Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ [base case]. This statement explicitly links the base case and inductive step to confirm the statements validity for all relevant values of n, solidifying your proof and earning full credit.
Look for keywords or phrases like prove by induction, show by mathematical induction, or for all integers n ≥ [value]. The question will almost always explicitly state that induction is the required method. Additionally, questions involving sequences, series, or divisibility for all integers are often solved using mathematical induction.
First, carefully review your base case to ensure its valid. Then, meticulously examine your inductive step, paying close attention to how youve used the inductive hypothesis. Substitute a few small values of n (beyond the base case) into the original statement to see if it holds true; this can help identify algebraic errors. Finally, ensure your concluding statement clearly summarizes your findings and explicitly states the range of n for which the statement is true.

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