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.