Q292 · Practice questionTechnology-freeSimple familiar1 mark
QUESTION 292
A student verifies a proposition for n=1, then proves that if it holds for n=k, it holds for n=k+2. What can this establish without another base case?
(A)
The proposition holds for every positive even integer.
(B)
The proposition has been disproved.
(C)
The proposition holds for every positive integer.
(D)
The proposition holds for every positive odd integer.
WORKED SOLUTION
1 markAnswer D
ANSWER
D. The proposition holds for every positive odd integer.
Worked solution
Starting at 1 and advancing by 2 reaches 1,3,5,... . To cover even integers as well, a second initial case such as n=2 is needed.
Equivalent justified methods accepted; respect any requested proof method.
Exact values unless specified. Sketches assessed by mathematical features, not artistic quality.
Select D.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabus