STEP 2006 Solutions Thread

Thank you ever so much, as a follow up. How do we know that the above integer is infact the nearest one?

(sorry, it might be obvious)

It is it because (2N-0.5)^(-k) is less than half?

Sorry to keep bothering you and I promise this will be the last question, I don't understand the recurrence relation SimonM wrote. How does k fit into the recurrence relation?

Thanks

Since you've deleted your post (don't do that! It makes the discussion very difficult to follow for anyone reading it later) I can't see exactly what SimonM did as I reply. But it's basically setting up a 2nd order recurrence relation with fundamental solutions corresponding to N+sqrt(N^2-1) and it's reciprocal.

If you didn't understand that, don't worry - it's not in the A-level syllabus and I'm sure is not the expected solution. Instead of doing that, you should be able to generalise what you did in the first part to show that Ak+1/Ak is an integer.

There were over 40 questions set in 2006, it would be helpful for you to state which one you are talking about!

So in the STEP III 2006 Q9 where did 2v squared come from? I understand there is a v squared and (rtheta) squared but I don't get the 2 behind the v, thanks.

The speed (squared) of B is
v^2 + (r*thetadot)^2
where v = rdot, and the second v^2 is obviously P.

Oh my god, those are actually components of velocity of B, now I finally understand
That is so amazing