# Fp1 Proof by Induction

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#1
Proof in induction questions are my pet peeve and I never seem to understand the method given in the markschemes. However, I learned a new method recently and have been using that to solve these questions and it seems perfectly logical and coherent to me.

I was just curious whether this method is accepted and if I would score full marks if I use it in exam. I have attached it below.
0
2 years ago
#2
(Original post by Fasih178)
Proof in induction questions are my pet peeve and I never seem to understand the method given in the markschemes. However, I learned a new method recently and have been using that to solve these questions and it seems perfectly logical and coherent to me.

I was just curious whether this method is accepted and if I would score full marks if I use it in exam. I have attached it below.
Your method is fine and that proof would score full marks in an FP1 exam. A few things to improve:

- Label expressions so that your working makes sense. So instead of saying "For n=k+1", you could say

Then you can refer to later. In your working, after "sub in" it wasn't clear what the next line was but if you labelled your expression it would have made more sense.

- Your are mixing up the symbol and the symbol. The 5th line of working should have an and a lot of the from line 9 should be signs. means "implies" i.e. if this is true then this is true. When you read through your working it should make sense gramatically. If you need more explanation let us know.

- Your 1's looks like 3's and sometimes also look like 2's - I had to read your working a few times to understand it. Be careful with this.
Last edited by Notnek; 2 years ago
2
#3
(Original post by Notnek)
Your method is fine and that proof would score full marks in an FP1 exam. A few things to improve:

- Label expressions so that your working makes sense. So instead of saying "For n=k+1", you could say

Then you can refer to later. In your working, after "sub in" it wasn't clear what the next line was but if you labelled your expression it would have made more sense.

- Your are mixing up the symbol and the symbol. The 5th line of working should have an and a lot of the from line 9 should be signs. means "implies" i.e. if this is true then this is true. When you read through your working it should make sense gramatically. If you need more explanation let us know.

- Your 1's looks like 3's and sometimes also look like 2's - I had to read your working a few times to understand it. Be careful with this.
Wow I was not expecting such a detailed reply, thank you so much. It's a relief to know that this method is perfectly feasible because I just can't seem to grasp the ones given in the mark schemes.

I profusely use the right arrow sign in all papers, I guess I've been applying it all wrong. I'm also glad you mentioned the flaw with my 1's because someone else remarked something similar a while ago but I treated his comment like water off a duck's back. I would sure amend the way I write 1 from now on lest I end up losing marks for something so silly.

How can I possibly need any more explanation after such a detailed response buddy, thanks a lot, truly.
1
2 years ago
#4
Completely random question, what pen do you use?
I like the way it looks
0
2 years ago
#5
(Original post by Fasih178)
Wow I was not expecting such a detailed reply, thank you so much. It's a relief to know that this method is perfectly feasible because I just can't seem to grasp the ones given in the mark schemes.

I profusely use the right arrow sign in all papers, I guess I've been applying it all wrong. I'm also glad you mentioned the flaw with my 1's because someone else remarked something similar a while ago but I treated his comment like water off a duck's back. I would sure amend the way I write 1 from now on lest I end up losing marks for something so silly.

How can I possibly need any more explanation after such a detailed response buddy, thanks a lot, truly.
i agree with Notnek's comments; in addition i would point out that you have used ℝ instead of ℤ+ or ℕ several times.
2
#6
(Original post by yoyo polo)
Completely random question, what pen do you use?
I like the way it looks
It's a Pelikano fountain pen, pretty smooth but can be rather stubborn if you leave it open to air for a few minutes.
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