Difference between revisions of "Sum of Fibonacci numbers"
From specialfunctionswiki
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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== | ||
Revision as of 00:28, 24 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.
