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