Difference between revisions of "Sum of Lucas numbers"
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(Created page with "==Theorem== The following formula holds: $$\displaystyle\sum_{k=1}^n L(k) = L(n+2)-3,$$ where $L(k)$ denotes the $k$th Lucas number. ==Proof== ==References...") |
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==References== | ==References== | ||
| − | * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Sum of Fibonacci numbers|next= | + | * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Sum of Fibonacci numbers|next=F(n+1)F(n-1)-F(n)^2=(-1)^n}} |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 00:19, 25 May 2017
Theorem
The following formula holds: $$\displaystyle\sum_{k=1}^n L(k) = L(n+2)-3,$$ where $L(k)$ denotes the $k$th Lucas number.
