Difference between revisions of "N^2=T(n)+T(n-1)"
From specialfunctionswiki
(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...") |
|||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=T(n+1)=T(n)+n+1|next= | + | * {{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))}} |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 01:24, 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.
