Difference between revisions of "Sum of even indexed Fibonacci numbers"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=1}^n F_{2k} = F_{2n+1}-1,$$ where $F_{2k}$ denotes a Fibonacci number. ==Proof== ==Ref...") |
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The following formula holds: | The following formula holds: | ||
$$\displaystyle\sum_{k=1}^n F_{2k} = F_{2n+1}-1,$$ | $$\displaystyle\sum_{k=1}^n F_{2k} = F_{2n+1}-1,$$ | ||
| − | where $F_{2k}$ denotes | + | where $F_{2k}$ denotes the $2k$th [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
Latest revision as of 00:30, 24 May 2017
Theorem
The following formula holds: $$\displaystyle\sum_{k=1}^n F_{2k} = F_{2n+1}-1,$$ where $F_{2k}$ denotes the $2k$th Fibonacci number.
