How can the sum of a Fibonacci series to the nth term be calculated?

[heartyface]

hey:)
So I've been trying to calculate the sum of a fibonnaci series to the nth term...
like
a, b, a+b, a+2b, 2a+3b, 3a+5b, 5a+8b...
but then the series repeat themselves in this as well...
so
a1, a2, a3, a4, a5, a6...
is equal to
(excuse me for being uncapable of speaking latex the language of the gods...)
a1, a2, a1(a1)+a2(a2), a1(a2)+a2(a3), a1(a3)+a2(a4), a1(a4)+a2(a5)...
which is
a1, a2, a1^2+a2^2, a2(a1+a1^2+a2^2), a1^3+2a1a2^2+a1^2a2^2+a2^4...
(i could have made a mistake somewhere...)
so my point is
how... do you calculate the sum of a fibonnaci series to the nth term
thanks:)

 

[chiro]

Hey heartyface and welcome to the forums.

There is a formula for this and the process to derive the formula is a well known one (in the way that it has been known for a long time).

You should probably have a look at this [Google is your friend ;)]

http://en.wikipedia.org/wiki/Fibonacci_number