Difference between revisions of "N^2=T(n)+T(n-1)"
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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=T(n)^2=T(T(n))+T(T(n)-1)}} | + | * {{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
- V.E. Hoggatt, Jr and Marjorie Bicknell: Triangular numbers (1974)... (previous)... (next) $(1.3)$
