Q20 · Practice questionComplex familiar5 marks
QUESTION 20 (5 marks)
Use mathematical induction to prove that is divisible by 6 for every positive integer .
WORKED SOLUTION
5 marksPractice marking scheme
ANSWER
for every .
Worked solution
For , , which is divisible by 6.
Assume for some integer . Then Since is an integer, the expression is divisible by 6. By induction, the result holds for every positive integer .
Verifies the base case.
States the induction assumption.
Forms a useful rearrangement.
Factors as six times an integer.
Concludes by induction.
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