QCAA Specialist Mathematics Practice Questions - QCAA Specialist Mathematics (Units 3 & 4) Exam

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When proving by mathematical induction that 7^n - 1 is divisible by 6 for all positive integers n, assuming 7^k - 1 = 6M for some integer M, which expression correctly demonstrates the inductive step for n = k + 1?

7^{k+1} - 1 = 7(6M) - 1 7^{k+1} - 1 = 6(7M + 1) 7^{k+1} - 1 = 6(7M - 1) 7^{k+1} - 1 = 42M - 1

Correct Answer:

7^{k+1} - 1 = 6(7M + 1)

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