Difference between revisions of "Sum of Fibonacci numbers"
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The following formula holds: | The following formula holds: | ||
$$\displaystyle\sum_{k=1}^n F_k = F_{n+2}-1,$$ | $$\displaystyle\sum_{k=1}^n F_k = F_{n+2}-1,$$ | ||
| − | where $F_k$ denotes | + | where $F_k$ denotes the $k$th [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Lucas numbers|next=Sum of Lucas numbers}} | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 00:15, 25 May 2017
Theorem
The following formula holds: $$\displaystyle\sum_{k=1}^n F_k = F_{n+2}-1,$$ where $F_k$ denotes the $k$th Fibonacci number.
