Maths Induction (1 Viewer)

[madsam]

Ok, we've been given a rather hard maths induction question that is too long and stuff to post up.
Anyway, i can do all of it except for the prove for n = k+1, like i can prove for n = 1,2,3 and stuff

My question is, since these things are marked out of 4 or 5 generally, and one mark is in the conclusion, if i cant prove for n = k+1, but then i go and right a conclusion saying, since it is true for n = 1,2,3 and n = k+1 it must be true for all n, would i still get a mark? Or would they go no, since you never proved it for n = k+1 you dont get a mark?

Does it matter that your supposed to get a mark for correctly writing the conclusion?

 

[Trebla]

I'm not sure how your teachers mark them, but the HSC marking scheme usually goes like this for an induction question:

A typical 3 mark induction question:
- Verification of initial case (1 mark)
- State assumption n = k (1 mark)
- Prove n = k + 1 using the assumption (1 mark)

A harder 4 mark induction question:
- Verification of initial case (1 mark)
- State assumption n = k (1 mark)
- Prove n = k + 1 using the assumption (2 marks)

Note that there are no marks allocated to the conclusion for the official HSC exams, however school teachers may allocate them in their assessments at their discretion. Also, most induction questions are at least 3 marks and most do not exceed 4 marks in value.

 

[shaon0]

Ok, we've been given a rather hard maths induction question that is too long and stuff to post up.
Anyway, i can do all of it except for the prove for n = k+1, like i can prove for n = 1,2,3 and stuff

My question is, since these things are marked out of 4 or 5 generally, and one mark is in the conclusion, if i cant prove for n = k+1, but then i go and right a conclusion saying, since it is true for n = 1,2,3 and n = k+1 it must be true for all n, would i still get a mark? Or would they go no, since you never proved it for n = k+1 you dont get a mark?

Does it matter that your supposed to get a mark for correctly writing the conclusion?

You wouldn't get a mark for proving for some finite integral values of n.
You have to prove for: {n E Z: n>= 1} as a usual case.

 

[Tsylana]

I thought in a typical 3 mark induction question

you'd usually get 1 mark for the initial process of the n = k+1 and simplifying
another for substituting or using the assumption...
and a 3rd mark for justifying the statement for n = k+1...

so all 3 marks are allocated in part 3...? though u can the other steps are needed to get full marks... the steps themselves dont get you any marks.