For the following function f with domain N determine a formula for f(n) and use mathematical induction to prove your conclusion:
For a1,a2 in R, arbitrary, let f(1)=a1 and f(2)=a2. For n>2 f(n)=- f(n-2)/n(n-1)
I calculated the first few values as :
I was going to define this piecewise, since a1 goes with the odd n and a2 is paired with even ones. I've come up with
a1/n(n-1)(n-2)(n-3) for even n
a2/n(n-1)(n-2)(n-3) for odd n
I'm not really sure how to address the changing sign however. I feel like I should use -1 to some power, but I'm not sure how to approach it.