Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers.
Follow Math Help Forum on Facebook and Google+
Originally Posted by Chris11 Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers. $\displaystyle \sum_{i=1}^n F_i = F_{n+2}-1 $ This can be shown by induction or by the explicit formula for the Fibonacci sequence.
Thanks.
Proof: $\displaystyle F_1=F_3-F_2$ $\displaystyle F_2=F_4-F_3$ $\displaystyle F_3=F_5-F_4$ . . . $\displaystyle F_{n-1}=F_{n+1}-F{n}$ $\displaystyle F_n=F_{n+2}-F_{n+1}$ now add them... what you get?
View Tag Cloud