f(0)=0f(1)=1f(k)=f(k-1)+f(k-2)当K为7的时候等于多少

Question

f(0)=0 f(1)=1 f(k)=f(k-1)+f(k-2) 当K为7的时候等于多少

Answer 1

f(0)=0 f(1)=1 f(k)=f(k-1)+f(k-2)
则当k=7时
f(7)=f(6)+f(5)
=f(5)+f(4)+f(5)
=2[f(4)+f(3)]+f(3)+f(2)
=2f(4)+3f(3)+f(2)
=2[f(3)+f(2)]+3[f(2)+f(1)]+f(1)+f(0)
=2f(3)+5f(2)+4f(1)+f(0)
=2[f(2)+f(1)]+5[f(1)+f(0)]+4f(1)+f(0)
=2f(2)+11f(1)+6f(0)
=2[f(1)+f(0)]+11f(1)+6f(0)
=13f(1)+8f(0)
=13x1+8x0
=13