With divisibility proof questions, can you use the method where you assume f(k) is divisible by 5 and so have f(k)=5m (rearranging it and substituting into f(k+1), and still get full marks? It's not a popular method like the f(k+1)-f(k) method but I often find it easier, don't want to risk not getting full marks though.
For proof by induction divisibility questions.... Not sure how to word it so I will give an example.. Prove that 3^(2n+3) + 3n +2 is divisible by 9 (probably not true) Can you in your induction step go straight to : f(k+1) - 9f(k) = blah blah To cancel the 3^(2n+3) term or do you need to start with a coefficient of one?
you would have to say f(k+1)=..... or f(k+1)-f(k)=....... and then end up making it f(k+1)
Is part c part of the spec because it's the only part of the question I can't do and I've never seen anything similar in a past paper. Also if it is how do you do it?
With divisibility proof questions, can you use the method where you assume f(k) is divisible by 5 and so have f(k)=5m (rearranging it and substituting into f(k+1), and still get full marks? It's not a popular method like the f(k+1)-f(k) method but I often find it easier, don't want to risk not getting full marks though.
Haven't seen that method in mark schemes so i am not sure. Would go for f)k+1-f(k) as it is popular and usually gets you the six marks. Good luck
Is part c part of the spec because it's the only part of the question I can't do and I've never seen anything similar in a past paper. Also if it is how do you do it?
Haven't seen this ever before, I think that it's outside the spec. What one are you looking at?
Is part c part of the spec because it's the only part of the question I can't do and I've never seen anything similar in a past paper. Also if it is how do you do it?
if you don't mind me asking what paper is this from?
you would have to say f(k+1)=..... or f(k+1)-f(k)=....... and then end up making it f(k+1)
Oh really I've always practiced by doing f(k+1) - xf(k) = Then adding the xf(k) at the end. And saying if f(k) is divisible, xf(k) is divisible and so true for n=k+1
Maybe in the exam I'll try and do it both ways. They credit your highest scoring method right?
Oh really I've always practiced by doing f(k+1) - xf(k) = Then adding the xf(k) at the end. And saying if f(k) is divisible, xf(k) is divisible and so true for n=k+1
Maybe in the exam I'll try and do it both ways. They credit your highest scoring method right?
I use that method because i have seen it in almost all the mark schemes. I am not sure about your method but if thats the one you are comfortable with use it
I use that method because i have seen it in almost all the mark schemes. I am not sure about your method but if thats the one you are comfortable with use it
It is basically the same thing only that you get the xf(k) on the right hand side rather than the left. that is f(k+1)-f(k)=8f(k)+8(30k+5) for example. then you move the f(k) to the right. You should be credited for your method if you end up with the correct proof. THe mark scheme gives many proofs. My advice would be check in other mark schemes as well. Good luck.
I use that method because i have seen it in almost all the mark schemes. I am not sure about your method but if thats the one you are comfortable with use it
Is part c part of the spec because it's the only part of the question I can't do and I've never seen anything similar in a past paper. Also if it is how do you do it?
It's more FP3, than FP1. I wouldn't worry about it