0,1,1,2,3,5,8...

Just finished Chapter A1 of MST221 in which we get to poke around that set of numbers up there, the Fibonacci sequence, an example of a second order recurrence system. All quite interesting stuff and I didn't have too many problems getting my head around the sums including the derivation of a closed form for such sequences - which given the struggle I had with wrapping my poor dragony brain around the same derivation for first order sequences last year I was rather happy with.

I did have a bit of an issue with the algebra when doing the exercise to derive a closed form for a Cassini identity as the OU have started truncating their solutions and I am assuming just expect you to be able to follow this stuff by now.... bit like this...



Anyway a quick email to the tutor (and a same day response - great service!) gave me a poke in the right direction with something that is bleeding obvious once you've been shown it, which is.

 n-1                          n       n+1
a     is a common factor of  a   and a

so 2 is a common factor of 4 and 8, 3 is a common factor of 9 and 27, and so on.

I was even happier when Question 2 of the TMA was on just such an identity.

So, onto conics