I would greatly appreciate some direction or hints to finish this problem.
Let n be a natural number such that n>5. Show that Fn=5Fn-4+3Fn-5. (Where all n, n-4, and n-5 are subscripts of F)
I know I need to proceed by way of strong mathematical induction.
Base Case: Suppose n=6. Then, F(6)=5F(6-4)+3F(6-5)= 5F(2)+3F(1).
Now I'm stuck. I'm not even sure how to establish the base case. I realize typically you just show that the statement is true for a variable. However, I don't know how to show the equivalency here. Should I set the Fn equal to a value?
I appreciate any help.!