an=2an-1-4an-2 an=an-2+an-3 an=nan-1+an-2 Working with LH RR with CC and degree 2 That feels like it jumps out of nowhere. Let’s focus on what it says, time allowing we will try to show it makes sense (or at least a bit of sense). The proof is on pages 515 and 516 of the text. Consider the Fibonacci sequence defined by an=an-1+an-2. This is saying we need to find the roots of the characteristic equation and then the solution for this relation is of the form , where r1 and r2 are those roots. Notice that α is just an arbitrary constant (that we’d have to figure out…) an=3an-1-2an-2; a0=3, Last time we worked out examples 3 and 4 from the text. Let’s try this one: a1=4 Repeated roots Let’s do an=6an-1 -9an-2 where a0=1 and a1=6 What is the characteristic equation?
an=2an-1-4an-2 an=an-2+an-3 an=nan-1+an-2 Working with LH RR with CC and degree 2 That feels like it jumps out of nowhere. Let’s focus on what it says, time allowing we will try to show it makes sense (or at least a bit of sense). The proof is on pages 515 and 516 of the text. Consider the Fibonacci sequence defined by an=an-1+an-2. This is saying we need to find the roots of the characteristic equation and then the solution for this relation is of the form , where r1 and r2 are those roots. Notice that α is just an arbitrary constant (that we’d have to figure out…) Last time we worked out examples 3 and 4 from the text. Let’s try this one: an=3an-1-2an-2; a0=3, a1=4 Repeated roots Let’s do an=6an-1 -9an-2 where a0=1 and a1=6 What is the characteristic equation?
203L18S16.docx