Difference between revisions of "Sum of odd indexed Fibonacci numbers"
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m (Tom moved page Sum of odd Fibonacci numbers to Sum of odd indexed Fibonacci numbers) |
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The following formula holds: | The following formula holds: | ||
$$\displaystyle\sum_{k=1}^n F_{2k+1} = F_{2n+2},$$ | $$\displaystyle\sum_{k=1}^n F_{2k+1} = F_{2n+2},$$ | ||
| − | where $F_{2k+1}$ denotes | + | where $F_{2k+1}$ denotes the $2k+1$st [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
Latest revision as of 00:29, 24 May 2017
Theorem
The following formula holds: $$\displaystyle\sum_{k=1}^n F_{2k+1} = F_{2n+2},$$ where $F_{2k+1}$ denotes the $2k+1$st Fibonacci number.
