Difference between revisions of "Sum of odd indexed Fibonacci numbers"
From specialfunctionswiki
(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=1}^n F_{2k+1} = F_{2n+2},$$ where $F_{2k+1}$ denotes a Fibonacci number. ==Proof== ==R...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
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.
