Difference between revisions of "N^2=T(n)+T(n-1)"

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(Created page with "==Theorem== The following formula holds for $n=1,2,3,\ldots$: $$n^2=T(n)+T(n-1),$$ where $T(n)$ denotes the $n$th triangular number. ==Proof== ==Refer...")
 
 
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==References==
 
==References==
* {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=T(n+1)=T(n)+n+1|next=findme}}
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* {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=T(n+1)=T(n)+n+1|next=T(n)^2=T(T(n))+T(T(n)-1)}} $(1.3)$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 01:27, 30 May 2017

Theorem

The following formula holds for $n=1,2,3,\ldots$: $$n^2=T(n)+T(n-1),$$ where $T(n)$ denotes the $n$th triangular number.

Proof

References