Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers.

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- Jul 7th 2010, 05:50 PMChris11Sum of first n fibbonaci numbers
Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers.

- Jul 7th 2010, 06:05 PMchiph588@
- Jul 7th 2010, 06:54 PMChris11
Thanks.

- Jul 7th 2010, 07:01 PMAlso sprach Zarathustra
Proof:

$\displaystyle F_1=F_3-F_2$

$\displaystyle F_2=F_4-F_3$

$\displaystyle F_3=F_5-F_4$

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$\displaystyle F_{n-1}=F_{n+1}-F{n}$

$\displaystyle F_n=F_{n+2}-F_{n+1}$

now add them... what you get?