Difference between revisions of "Sum of Fibonacci numbers"

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(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=1}^n F_k = F_{n+2}-1,$$ where $F_k$ denotes the Fibonacci sequence. ==Proof== ==References== Category:...")
 
 
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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 the [[Fibonacci sequence]].
+
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.

Proof

References