求数列的通项公式:a0=0,a1=1,an=2an-1+an-2

问题描述:

求数列的通项公式:a0=0,a1=1,an=2an-1+an-2

an=2an-1+an-2,可以构造方程x^2=2x+1,x1=1-√2,x2=1+√2则an-(1-√2)an-1=(1+√2)[an-1-(1-√2)an-2]或 an-(1+√2)an-1=(1-√2)[an-1-(1+√2)an-2] 令bn=an-(1-√2)an-1,bn'=an-(1+√2)an-1 则bn=(...