Difference between revisions of "T(n)^2=T(T(n))+T(T(n)-1)"
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(Created page with "==Theorem== The following formula holds for $n=2,3,4,\ldots$: $$T(n)^2=T(T(n))+T(T(n-1)),$$ where $T(n)$ denotes the $n$th triangular number. ==Proof==...") |
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==Theorem== | ==Theorem== | ||
The following formula holds for $n=2,3,4,\ldots$: | The following formula holds for $n=2,3,4,\ldots$: | ||
| − | $$T(n)^2=T(T(n))+T(T(n-1 | + | $$T(n)^2=T(T(n))+T(T(n)-1),$$ |
where $T(n)$ denotes the $n$th [[triangular numbers|triangular number]]. | where $T(n)$ denotes the $n$th [[triangular numbers|triangular number]]. | ||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=N^2=T(n)+T(n-1)|next= | + | * {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=N^2=T(n)+T(n-1)|next=T(n+1)^2-T(n)^2=(n+1)^3}} $(1.4)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 01:30, 30 May 2017
Theorem
The following formula holds for $n=2,3,4,\ldots$: $$T(n)^2=T(T(n))+T(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) $(1.4)$
