Problem: If F(n)F(n)F(n) is a function such that F(1)=F(2)=F(3)=1F(1)=F(2)=F(3)=1F(1)=F(2)=F(3)=1, and such that F(n+1)=F(n)⋅F(n−1)+1F(n−2)F(n+1)=\dfrac{F(n) \cdot F(n-1)+1}{F(n-2)}F(n+1)=F(n−2)F(n)⋅F(n−1)+1​ for n≧3n \geqq 3n≧3, then F(6)F(6)F(6) is equal to
Answer Choices:
A. 222
B. 333
C. 777
D. 111111
E. 262626 Solution:
Substitution yields F(4)=2,F(5)=3F(4)=2, F(5)=3F(4)=2,F(5)=3, and finally F(6)=7F(6)=7F(6)=7.