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(n1)+F(n2) 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?
(In reply to
what is being asked??? by Jim)
It is asking for a formula relating these partial sums up to a given term k, to the value of k chosenthat is, as a function of k. So for example if k is 5, the formula for the first question would give you 0+1+1+2+3+5 = 12. The formula given so far for that is F(k+2); in this instance that is F(5+2)=F(7)=12.

Posted by Charlie
on 20040715 22:00:20 