Difference between revisions of "Sum of squares of Fibonacci numbers"
From specialfunctionswiki
(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...") |
|||
| (One intermediate revision by the same user not shown) | |||
| Line 2: | Line 2: | ||
The following formula holds: | The following formula holds: | ||
$$\displaystyle\sum_{k=1}^n F_k^2 = F_n F_{n+1},$$ | $$\displaystyle\sum_{k=1}^n F_k^2 = F_n F_{n+1},$$ | ||
| − | where $F_k$ denotes | + | where $F_k$ denotes the $k$th [[Fibonacci numbers|Fibonacci number]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
| + | * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)|next=L(n)^2-5F(n)^2=4(-1)^n}} | ||
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 00:35, 25 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.
