I have been to various seminars and spoken about this issue with several different HSC markers.
Induction questions are worth 3 marks, and the 3 marks are allocated as follows:
1st mark: Proving the statement is true for n=1.
2nd mark: Correctly integrating your assumption (assume true for some n = k) into the proof for n = k + 1.
3rd mark: Breaking down the proof to a point where it is clear that if it is true for n = k, it is true for n = k + 1.
Technically you could leave it there and you would be awarded full marks. At most, write "therefore true for all integers n >= 1 by induction".
Induction questions are worth 3 marks, and the 3 marks are allocated as follows:
1st mark: Proving the statement is true for n=1.
2nd mark: Correctly integrating your assumption (assume true for some n = k) into the proof for n = k + 1.
3rd mark: Breaking down the proof to a point where it is clear that if it is true for n = k, it is true for n = k + 1.
Technically you could leave it there and you would be awarded full marks. At most, write "therefore true for all integers n >= 1 by induction".
