The Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, in which each number is the sum of the two previous, is defined as F(0)=0, F(1)=1, and F(n)=F(n-1)+F(n-2) for n>1.

What is the sum of F(0)+F(1)+F(2)+...+F(k)?
What is the sum of F(0)^2+F(1)^2+F(2)^2+...+F(k)^2?

Ó F(k)^2 as above is:

F(k)^2 * (1 + (F(k-1)/F(k))

Very neat

Posted by Hew BG on 2004-07-16 07:25:19