Homework 9, due Friday, February 4, 2011

[1] Let Tn be the sum of the squares of the first n Fibonacci numbers: Tn = F12 + ... + Fn2.
In class we were trying to find a formula for Tn. Recall that we made a table:
n	1	2	3	4	5	6	7	8	9
Fn	1	1	2	3	5	8	13	21	34
Tn	1	2	6	15	40	104	etc
Tn	1	1*2	2*3	3*5	5*8	8*13	etc
We noticed in class that T4 = 15 = 3*5 = F4*F5.

(a) Write down a formula for Tn so that when when n = 4 we get T4 = F4*F5 .

(b) Check your formula for at least two larger values of n to see if it works.