mathematical induction step 4 (1 Viewer)

[natnat96]

just wondering, do you lose marks for omitting step 4 from induction? the one about if it is true for n=k, then it must be true etc.
and can we just use the same one for all induction types ?


since when did maths require essays -_-

 

[rainlewis]

It depends on how your teacher marks it, however, in the HSC you must write it. You dont gain marks for it but you will most likely lose a mark if you dont write it. Its not long, just learn a simple basic one like:
Since true for n = 1 and true for n = k,
Proven true for n = k +1, it must also be true for n = 2, 3, 4 etc.
Thus, the proposition must be true for all values of k, where k is greater than or equal to 1.

There are obviously slight variations to the statement depending on the question of course, but that is the most basic.

 

[asianese]

You can shorten that.

Say:

Hence true for n>=1 by mathematical induction.

Done.

 

[Trebla]

It depends on how your teacher marks it, however, in the HSC you must write it. You dont gain marks for it but you will most likely lose a mark if you dont write it. Its not long, just learn a simple basic one like:
Since true for n = 1 and true for n = k,
Proven true for n = k +1, it must also be true for n = 2, 3, 4 etc.
Thus, the proposition must be true for all values of k, where k is greater than or equal to 1.

There are obviously slight variations to the statement depending on the question of course, but that is the most basic.

Should say "IF it is true for n = k". Remember that the case for n = k is assumed, not proven as true.

In the HSC, the conclusion is not marked, therefore it is not necessary. Obviously between schools and individual teachers this criteria may differ.

 

[GoldyOrNugget]

You can shorten that.

Say:

Hence true for n>=1 by mathematical induction.

Done.

Eek. Wouldn't count on this, especially since it's mathematically false. You should at least specify integer values of n.

 

[Capt Rifle]

I'm pretty sure you won't get full mark, it requires suitable reasoning.

 

[TimeGoesTooFast]

Don't think you can skip the step as it's a conclusion to your question but you can always leave out "Step4" .

 

[Omed62]

just wondering, do you lose marks for omitting step 4 from induction? the one about if it is true for n=k, then it must be true etc.
and can we just use the same one for all induction types ?


since when did maths require essays -_-

bro are you stupid or what... use you brain of course you will lose mark maybe like 1 mark. so make sure you right the last step as well. for example, By the principle of mathematics induction s(n) is true for all positive integers n> 1.

 

[Omed62]

People here are stupid... dont listen to anyone here... make sure you write the last step because you will lose a mark? I am sure about this.

 

[Immortalp00n]

Since proven true for n=1, assumed true for n=k and proven true for n=k+1, Sn is true for all positive integers n>=1
is it that hard?

 

[Capt Rifle]

memorise a common statement to use for all exams man

 

[funnytomato]

some teachers are very fussy about it

 

[RealiseNothing]

HSC only needs "hence true for all natural numbers by mathematical induction".

 

[Nws m8]

You can shorten that.

Say:

Hence true for n>=1 by mathematical induction.

Done.

I don't think you can do that for 3u

 

[TimeGoesTooFast]

bro are you stupid or what... use you brain of course you will lose mark maybe like 1 mark. so make sure you right the last step as well. for example, By the principle of mathematics induction s(n) is true for all positive integers n> 1.

Says the guy that couldn't even do an easy Ext 2 TAKE HOME ASSIGNMENT.

 

[Trebla]

If they really did deduct marks for having an incorrect or no conclusion, then it would be noted in the notes from the marking centre.

The sample answers do not have the full conclusion and several years ago in one year (I don't remember which one) it was commented (I think from the notes from the marking centre) that such a lengthy conclusion was not necessary and sometimes were written incorrectly (though I think no marks were deducted for that).

Also, from the marking criteria note that:

- 3 marks are awarded for a 'Complete induction proof'

- 2 marks were awarded for 'Makes some progress in the induction step or equivalent' or 'Makes substantial progress' or 'Attempts to do induction step'

This seems to indicate that simply completing the proof for n = k + 1 will get you the full 3 marks and an incomplete proof for n = k + 1 will get you 2 marks. The criteria does not mention anything about having a complete proof for n = k + 1 without a conclusion being awarded 2 marks.

Common sense should also dictate that a complete proof for n = k + 1 with no conclusion should not be awarded the same mark value as having an incomplete proof for n = k + 1 with no conclusion.

Remember though, we are talking about HSC marking. Marking by your school is a different matter altogether.

 

[planino]

Says the guy that couldn't even do an easy Ext 2 TAKE HOME ASSIGNMENT.

^

 

[Lieutenant_21]

bro are you stupid or what... use you brain of course you will lose mark maybe like 1 mark. so make sure you right the last step as well. for example, By the principle of mathematics induction s(n) is true for all positive integers n> 1.

write*
Tell us about your experience at JRAHS. You must be feeling really dumb there.

@OP: My tutor says it is only require for 3U and he is a HSC marker but my school teacher says it is important to always have a full statement as it shows that you understand the concept of induction. It is safer to just write the statement, it is only 1-2 lines.

 

[natnat96]

okay thanks and for the idiots that asked me if im stupid, gtfo off this site if u dont want to help others !

 

[Lieutenant_21]

okay thanks and for the idiots that asked me if im stupid, gtfo off this site if u dont want to help others !

Don't worry about him, everyone hates him here, he will hopefully get the fuck out and leave.