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 a [[Fibonacci sequence|Fibonacci number]].
  
 
==Proof==
 
==Proof==

Revision as of 02:23, 15 September 2016

Theorem

The following formula holds: $$\displaystyle\sum_{k=1}^n F_k = F_{n+2}-1,$$ where $F_k$ denotes a Fibonacci number.

Proof

References